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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Khemani%2C+V&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Khemani%2C+V&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Khemani%2C+V&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.13164">arXiv:2501.13164</a> <span> [<a href="https://arxiv.org/pdf/2501.13164">pdf</a>, <a href="https://arxiv.org/format/2501.13164">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Quantum chaos at finite temperature in local spin Hamiltonians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Langlett%2C+C+M">Christopher M. Langlett</a>, <a href="/search/quant-ph?searchtype=author&query=Jonay%2C+C">Cheryne Jonay</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Rodriguez-Nieva%2C+J+F">Joaquin F. Rodriguez-Nieva</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2501.13164v1-abstract-short" style="display: inline;"> Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes, quantum chaos has been primarily understood through the correspondence between the eigensystem statistics of midspectrum eigenstates and the universal statistics de… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.13164v1-abstract-full').style.display = 'inline'; document.getElementById('2501.13164v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.13164v1-abstract-full" style="display: none;"> Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes, quantum chaos has been primarily understood through the correspondence between the eigensystem statistics of midspectrum eigenstates and the universal statistics described by random matrix theory (RMT). However, this correspondence no longer holds for finite-temperature eigenstates. Here we show that the statistical properties of finite-temperature eigenstates of quantum chaotic Hamiltonians can be accurately described by pure random states constrained by a local charge, with the average charge density of the constrained random state ensemble playing the same role as the average energy density of the eigenstates. By properly normalizing the energy density using a single Hamiltonian-dependent parameter that quantifies the typical energy per degree of freedom, we find excellent agreement between the entanglement entropy statistics of eigenstates and that of constrained random states. Interestingly, in small pockets of Hamiltonian parameter phase space which we previously identified as `maximally chaotic' [PRX 14, 031014 (2024)], we find excellent agreement not only at the level of the first moment, including O(1) corrections, but also at the level of statistical fluctuations. These results show that notions of maximal chaos -- in terms of how much randomness eigenstates contain -- can still be defined at finite temperature in physical Hamiltonian models away from semi-classical and large-$N$ limits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.13164v1-abstract-full').style.display = 'none'; document.getElementById('2501.13164v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7+3 pages, 3+2 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.13248">arXiv:2412.13248</a> <span> [<a href="https://arxiv.org/pdf/2412.13248">pdf</a>, <a href="https://arxiv.org/format/2412.13248">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> </div> <p class="title is-5 mathjax"> Topological Quantum Spin Glass Order and its realization in qLDPC codes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Placke%2C+B">Benedikt Placke</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Breuckmann%2C+N+P">Nikolas P. Breuckmann</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.13248v1-abstract-short" style="display: inline;"> Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error correction. Here, we introduce the concept of topological quantum spin glass (TQSG) order which marries these two notions, exhibiting both the complex energy landscap… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.13248v1-abstract-full').style.display = 'inline'; document.getElementById('2412.13248v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.13248v1-abstract-full" style="display: none;"> Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error correction. Here, we introduce the concept of topological quantum spin glass (TQSG) order which marries these two notions, exhibiting both the complex energy landscapes of spin glasses, and the quantum memory and long-range entanglement characteristic of topologically ordered systems. Using techniques from coding theory and a quantum generalization of Gibbs state decompositions, we show that TQSG order is the low-temperature phase of various quantum LDPC codes on expander graphs, including hypergraph and balanced product codes. Our work introduces a topological analog of spin glasses that preserves quantum information, opening new avenues for both statistical mechanics and quantum computer science. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.13248v1-abstract-full').style.display = 'none'; document.getElementById('2412.13248v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13+28 pages, 3+5 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.09598">arXiv:2412.09598</a> <span> [<a href="https://arxiv.org/pdf/2412.09598">pdf</a>, <a href="https://arxiv.org/format/2412.09598">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Bottlenecks in quantum channels and finite temperature phases of matter </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Placke%2C+B">Benedikt Placke</a>, <a href="/search/quant-ph?searchtype=author&query=Breuckmann%2C+N+P">Nikolas P. Breuckmann</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.09598v1-abstract-short" style="display: inline;"> We prove an analogue of the "bottleneck theorem", well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel's steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.09598v1-abstract-full').style.display = 'inline'; document.getElementById('2412.09598v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.09598v1-abstract-full" style="display: none;"> We prove an analogue of the "bottleneck theorem", well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel's steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time in terms of an appropriately defined "quantum bottleneck ratio". Importantly, this bottleneck ratio involves not only the probabilities of the relevant subspaces, but also the size of off-diagonal matrix elements between them. For low-temperature quantum many-body systems, we use the bottleneck theorem to bound the performance of any quasi-local Gibbs sampler. This leads to a new perspective on thermally stable quantum phases in terms of a decomposition of the Gibbs state into multiple components separated by bottlenecks. As a concrete application, we show rigorously that weakly perturbed commuting projector models with extensive energy barriers (including certain classical and quantum expander codes) have exponentially large mixing times. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.09598v1-abstract-full').style.display = 'none'; document.getElementById('2412.09598v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures, 10 pages supplementary material</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.04414">arXiv:2412.04414</a> <span> [<a href="https://arxiv.org/pdf/2412.04414">pdf</a>, <a href="https://arxiv.org/format/2412.04414">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cheng%2C+Z">Zihan Cheng</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+E">Eric Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Gullans%2C+M+J">Michael J. Gullans</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.04414v1-abstract-short" style="display: inline;"> Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical qubits is nontrivial due to the need for magic gates, which can require a large resource overhead. In this work, we propose an efficient approach to generate unitar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.04414v1-abstract-full').style.display = 'inline'; document.getElementById('2412.04414v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.04414v1-abstract-full" style="display: none;"> Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical qubits is nontrivial due to the need for magic gates, which can require a large resource overhead. In this work, we propose an efficient approach to generate unitary designs for encoded qubits in surface codes by applying local unitary rotations ("coherent errors") on the physical qubits followed by syndrome measurement and error correction. We prove that under some conditions on the coherent errors (notably including all single-qubit unitaries) and on the error correcting code, this process induces a unitary transformation of the logical subspace. We numerically show that the ensemble of logical unitaries (indexed by the random syndrome outcomes) converges to a unitary design in the thermodynamic limit, provided the density or strength of coherent errors is above a finite threshold. This "unitary design" phase transition coincides with the code's coherent error threshold under optimal decoding. Furthermore, we propose a classical algorithm to simulate the protocol based on a "staircase" implementation of the surface code encoder and decoder circuits. This enables a mapping to a 1+1D monitored circuit, where we observe an entanglement phase transition (and thus a classical complexity phase transition of the decoding algorithm) coinciding with the aforementioned unitary design phase transition. Our results provide a practical way to realize unitary designs on encoded qubits, with applications including quantum state tomography and benchmarking in error correcting codes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.04414v1-abstract-full').style.display = 'none'; document.getElementById('2412.04414v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15+3 pages, 8+2 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.02384">arXiv:2411.02384</a> <span> [<a href="https://arxiv.org/pdf/2411.02384">pdf</a>, <a href="https://arxiv.org/ps/2411.02384">ps</a>, <a href="https://arxiv.org/format/2411.02384">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=De+Roeck%2C+W">Wojciech De Roeck</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+Y">Yaodong Li</a>, <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.02384v1-abstract-short" style="display: inline;"> We generalize the proof of stability of topological order, due to Bravyi, Hastings and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians $H_0$ defined by $[[N,K,d]]$ LDPC codes which obey certain topological quantum order conditions: (i) code distance… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02384v1-abstract-full').style.display = 'inline'; document.getElementById('2411.02384v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.02384v1-abstract-full" style="display: none;"> We generalize the proof of stability of topological order, due to Bravyi, Hastings and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians $H_0$ defined by $[[N,K,d]]$ LDPC codes which obey certain topological quantum order conditions: (i) code distance $d \geq c \log(N)$, implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states; these include good quantum LDPC codes, and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasi-local on the interaction graph defined by $H_0$, and which can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the $O(1)$ smallest eigenvalues of $H_0$. The band originating from the smallest eigenvalue has $2^K$ states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth $未= C N e^{-螛(d)}$, which is tighter than the best known bounds even in the Euclidean case. We also obtain that the new ground state subspace is related to the initial code subspace by a quasi-local unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02384v1-abstract-full').style.display = 'none'; document.getElementById('2411.02384v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.03325">arXiv:2409.03325</a> <span> [<a href="https://arxiv.org/pdf/2409.03325">pdf</a>, <a href="https://arxiv.org/format/2409.03325">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Non-Uniform Noise Rates and Griffiths Phases in Topological Quantum Error Correction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Sriram%2C+A">Adithya Sriram</a>, <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+Y">Yaodong Li</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.03325v1-abstract-short" style="display: inline;"> The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence ca… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.03325v1-abstract-full').style.display = 'inline'; document.getElementById('2409.03325v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.03325v1-abstract-full" style="display: none;"> The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. In this work, we study effects of non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatio-temporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.03325v1-abstract-full').style.display = 'none'; document.getElementById('2409.03325v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 17 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.03280">arXiv:2409.03280</a> <span> [<a href="https://arxiv.org/pdf/2409.03280">pdf</a>, <a href="https://arxiv.org/format/2409.03280">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Absorbing state transitions with long-range annihilation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Bhattacharjee%2C+S">Sayak Bhattacharjee</a>, <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.03280v1-abstract-short" style="display: inline;"> We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, such as chemical reacti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.03280v1-abstract-full').style.display = 'inline'; document.getElementById('2409.03280v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.03280v1-abstract-full" style="display: none;"> We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, such as chemical reactions involving reagents with long-range electromagnetic interactions. They also increasingly play a role in the study of quantum dynamics, in which certain quantum protocols can be mapped to classical stochastic processes with long-range interactions: for example, state preparation or error correction processes aim to prepare ordered ground states, which requires removing point-like excitations in pairs via non-local feedback operations conditioned on a global set of measurement outcomes. We analytically and numerically describe features of absorbing phases and phase transitions in this family of classical models as pairwise annihilation is performed at larger and larger distances. Notably, we find that the two canonical absorbing-state universality classes -- directed-percolation and parity-conserving -- are endpoints of a line of universality classes with continuously interpolating critical exponents. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.03280v1-abstract-full').style.display = 'none'; document.getElementById('2409.03280v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5+8 pages, 3 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.15757">arXiv:2406.15757</a> <span> [<a href="https://arxiv.org/pdf/2406.15757">pdf</a>, <a href="https://arxiv.org/format/2406.15757">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.6.010327">10.1103/PRXQuantum.6.010327 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Perturbative stability and error correction thresholds of quantum codes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Li%2C+Y">Yaodong Li</a>, <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.15757v3-abstract-short" style="display: inline;"> Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general CSS codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.15757v3-abstract-full').style.display = 'inline'; document.getElementById('2406.15757v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.15757v3-abstract-full" style="display: none;"> Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general CSS codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized Z2 lattice gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative X or Z magnetic field. Motivated by error correction considerations, we define general order parameters for all such generalized Z2 lattice gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the LDPC condition and with a sufficiently large code distance, we prove the existence of a low temperature ordered phase of the corresponding lattice gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence to stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and time-like defects in the lattice gauge theory. A high free-energy cost of space-like defects corresponds to a successful "memory experiment" and suppresses the energy splitting among the ground states, while a high free-energy cost of time-like defects corresponds to a successful "stability experiment" and points to a nonzero gap to local excitations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.15757v3-abstract-full').style.display = 'none'; document.getElementById('2406.15757v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages + appendices. v2: updated references and acknowledgements. v3: made clarifications and fixed typos. published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 6, 010327 (2025) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.10344">arXiv:2406.10344</a> <span> [<a href="https://arxiv.org/pdf/2406.10344">pdf</a>, <a href="https://arxiv.org/format/2406.10344">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Phases and phase transition in Grover's algorithm with systematic noise </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Dowarah%2C+S">Sasanka Dowarah</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">Chuanwei Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Kolodrubetz%2C+M+H">Michael H. Kolodrubetz</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.10344v1-abstract-short" style="display: inline;"> While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm - Grover's algorithm for unordered search on $L$ qubits - in the presence of systematic noise. This allows us to write the behavior as a random Floquet… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.10344v1-abstract-full').style.display = 'inline'; document.getElementById('2406.10344v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.10344v1-abstract-full" style="display: none;"> While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm - Grover's algorithm for unordered search on $L$ qubits - in the presence of systematic noise. This allows us to write the behavior as a random Floquet unitary, which we show is well-characterized by random matrix theory (RMT). The RMT analysis enables analytical predictions for phases and phase transitions of the many-body dynamics. We find two separate transitions. At moderate disorder $未_{c,\mathrm{gap}}\sim L^{-1}$, there is a ergodicity breaking transition such that a finite-dimensional manifold remains non-ergodic for $未< 未_{c,\mathrm{gap}}$. Computational power is lost at a much smaller disorder, $未_{c,\mathrm{comp}} \sim L^{-1/2}2^{-L/2}$. We comment on relevance to non-systematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.10344v1-abstract-full').style.display = 'none'; document.getElementById('2406.10344v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 11 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.16831">arXiv:2402.16831</a> <span> [<a href="https://arxiv.org/pdf/2402.16831">pdf</a>, <a href="https://arxiv.org/format/2402.16831">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Physics of (good) LDPC Codes II. Product constructions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.16831v1-abstract-short" style="display: inline;"> We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various features on generic Euclidean and non-Euclidean graphs. These codes can serve as fixed-point limits for phases of matter. To build our machinery, we unpack various p… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.16831v1-abstract-full').style.display = 'inline'; document.getElementById('2402.16831v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.16831v1-abstract-full" style="display: none;"> We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various features on generic Euclidean and non-Euclidean graphs. These codes can serve as fixed-point limits for phases of matter. To build our machinery, we unpack various product constructions from the coding literature in terms of physical principles such as symmetries and redundancies, introduce a new cubic product, and combine these products with the ideas of gauging and Higgsing introduced in Part I. We illustrate the usefulness of this approach in finite Euclidean dimensions by showing that using the one-dimensional Ising model as a starting point, we can systematically produce a very large zoo of classical and quantum phases of matter, including type I and type II fractons and SPT phases with generalized symmetries. We also use the balanced product to construct new Euclidean models, including one with topological order enriched by translation symmetry, and another exotic fracton model whose excitations are formed by combining those of a fractal spin liquid with those of a toric code, resulting in exotic mobility constraints. Moving beyond Euclidean models, we give a review of existing constructions of good qLDPC codes and classical locally testable codes and elaborate on the relationship between quantum code distance and classical energy barriers, discussed in Part I, from the perspective of product constructions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.16831v1-abstract-full').style.display = 'none'; document.getElementById('2402.16831v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.16032">arXiv:2310.16032</a> <span> [<a href="https://arxiv.org/pdf/2310.16032">pdf</a>, <a href="https://arxiv.org/format/2310.16032">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The Physics of (good) LDPC Codes I. Gauging and dualities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.16032v1-abstract-short" style="display: inline;"> Low-depth parity check (LDPC) codes are a paradigm of error correction that allow for spatially non-local interactions between (qu)bits, while still enforcing that each (qu)bit interacts only with finitely many others. On expander graphs, they can give rise to ``good codes'' that combine a finite encoding rate with an optimal scaling of the code distance, which governs the code's robustness agains… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.16032v1-abstract-full').style.display = 'inline'; document.getElementById('2310.16032v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.16032v1-abstract-full" style="display: none;"> Low-depth parity check (LDPC) codes are a paradigm of error correction that allow for spatially non-local interactions between (qu)bits, while still enforcing that each (qu)bit interacts only with finitely many others. On expander graphs, they can give rise to ``good codes'' that combine a finite encoding rate with an optimal scaling of the code distance, which governs the code's robustness against noise. Such codes have garnered much recent attention due to two breakthrough developments: the construction of good quantum LDPC codes and good locally testable classical LDPC codes, using similar methods. Here we explore these developments from a physics lens, establishing connections between LDPC codes and ordered phases of matter defined for systems with non-local interactions and on non-Euclidean geometries. We generalize the physical notions of Kramers-Wannier (KW) dualities and gauge theories to this context, using the notion of chain complexes as an organizing principle. We discuss gauge theories based on generic classical LDPC codes and make a distinction between two classes, based on whether their excitations are point-like or extended. For the former, we describe KW dualities, analogous to the 1D Ising model and describe the role played by ``boundary conditions''. For the latter we generalize Wegner's duality to obtain generic quantum LDPC codes within the deconfined phase of a Z_2 gauge theory. We show that all known examples of good quantum LDPC codes are obtained by gauging locally testable classical codes. We also construct cluster Hamiltonians from arbitrary classical codes, related to the Higgs phase of the gauge theory, and formulate generalizations of the Kennedy-Tasaki duality transformation. We use the chain complex language to discuss edge modes and non-local order parameters for these models, initiating the study of SPT phases in non-Euclidean geometries. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.16032v1-abstract-full').style.display = 'none'; document.getElementById('2310.16032v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.15011">arXiv:2307.15011</a> <span> [<a href="https://arxiv.org/pdf/2307.15011">pdf</a>, <a href="https://arxiv.org/format/2307.15011">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.5.020304">10.1103/PRXQuantum.5.020304 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.15011v3-abstract-short" style="display: inline;"> Monitored quantum dynamics -- unitary evolution interspersed with measurements -- has recently emerged as a rich domain for phase structure in quantum many-body systems away from equilibrium. Here we study monitored dynamics from the point of view of an eavesdropper who has access to the classical measurement outcomes, but not to the quantum many-body system. We show that a measure of information… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.15011v3-abstract-full').style.display = 'inline'; document.getElementById('2307.15011v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.15011v3-abstract-full" style="display: none;"> Monitored quantum dynamics -- unitary evolution interspersed with measurements -- has recently emerged as a rich domain for phase structure in quantum many-body systems away from equilibrium. Here we study monitored dynamics from the point of view of an eavesdropper who has access to the classical measurement outcomes, but not to the quantum many-body system. We show that a measure of information flow from the quantum system to the classical measurement record -- the informational power -- undergoes a phase transition in correspondence with the measurement-induced phase transition (MIPT). This transition determines the eavesdropper's (in)ability to learn properties of an unknown initial quantum state of the system, given a complete classical description of the monitored dynamics and arbitrary classical computational resources. We make this learnability transition concrete by defining classical shadows protocols that the eavesdropper may apply to this problem, and show that the MIPT manifests as a transition in the sample complexity of various shadow estimation tasks, which become harder in the low-measurement phase. We focus on three applications of interest: Pauli expectation values (where we find the MIPT appears as a point of optimal learnability for typical Pauli operators), many-body fidelity, and global charge in $U(1)$-symmetric dynamics. Our work unifies different manifestations of the MIPT under the umbrella of learnability and gives this notion a general operational meaning via classical shadows. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.15011v3-abstract-full').style.display = 'none'; document.getElementById('2307.15011v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16+4 pages, 3 figures. v2: fixed error in Fig.1 panel labels. v3: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 5, 020304 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.16716">arXiv:2306.16716</a> <span> [<a href="https://arxiv.org/pdf/2306.16716">pdf</a>, <a href="https://arxiv.org/format/2306.16716">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.132.100401">10.1103/PhysRevLett.132.100401 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Prethermal stability of eigenstates under high frequency Floquet driving </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Burnell%2C+F">Fiona Burnell</a>, <a href="/search/quant-ph?searchtype=author&query=Chandran%2C+A">Anushya Chandran</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.16716v2-abstract-short" style="display: inline;"> Systems subject to high-frequency driving exhibit Floquet prethermalization, that is, they heat exponentially slowly on a time scale that is large in the drive frequency, $蟿_{\rm h} \sim \exp(蠅)$. Nonetheless, local observables can decay much faster via energy conserving processes, which are expected to cause a rapid decay in the fidelity of an initial state. Here we show instead that the fideliti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.16716v2-abstract-full').style.display = 'inline'; document.getElementById('2306.16716v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.16716v2-abstract-full" style="display: none;"> Systems subject to high-frequency driving exhibit Floquet prethermalization, that is, they heat exponentially slowly on a time scale that is large in the drive frequency, $蟿_{\rm h} \sim \exp(蠅)$. Nonetheless, local observables can decay much faster via energy conserving processes, which are expected to cause a rapid decay in the fidelity of an initial state. Here we show instead that the fidelities of eigenstates of the time-averaged Hamiltonian, $H_0$, display an exponentially long lifetime over a wide range of frequencies -- even as generic initial states decay rapidly. When $H_0$ has quantum scars, or highly excited-eigenstates of low entanglement, this leads to long-lived non-thermal behavior of local observables in certain initial states. We present a two-channel theory describing the fidelity decay time $蟿_{\rm f}$: the interzone channel causes fidelity decay through energy absorption i.e. coupling across Floquet zones, and ties $蟿_{\rm f}$ to the slow heating time scale, while the intrazone channel causes hybridization between states in the same Floquet zone. Our work informs the robustness of experimental approaches for using Floquet engineering to generate interesting many-body Hamiltonians, with and without scars. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.16716v2-abstract-full').style.display = 'none'; document.getElementById('2306.16716v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2 - published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 132, 100401 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.09333">arXiv:2306.09333</a> <span> [<a href="https://arxiv.org/pdf/2306.09333">pdf</a>, <a href="https://arxiv.org/format/2306.09333">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1126/science.adi7877">10.1126/science.adi7877 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamics of magnetization at infinite temperature in a Heisenberg spin chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rosenberg%2C+E">Eliott Rosenberg</a>, <a href="/search/quant-ph?searchtype=author&query=Andersen%2C+T">Trond Andersen</a>, <a href="/search/quant-ph?searchtype=author&query=Samajdar%2C+R">Rhine Samajdar</a>, <a href="/search/quant-ph?searchtype=author&query=Petukhov%2C+A">Andre Petukhov</a>, <a href="/search/quant-ph?searchtype=author&query=Hoke%2C+J">Jesse Hoke</a>, <a href="/search/quant-ph?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/quant-ph?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/quant-ph?searchtype=author&query=Drozdov%2C+I">Ilya Drozdov</a>, <a href="/search/quant-ph?searchtype=author&query=Erickson%2C+C">Catherine Erickson</a>, <a href="/search/quant-ph?searchtype=author&query=Klimov%2C+P">Paul Klimov</a>, <a href="/search/quant-ph?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/quant-ph?searchtype=author&query=Morvan%2C+A">Alexis Morvan</a>, <a href="/search/quant-ph?searchtype=author&query=Neeley%2C+M">Matthew Neeley</a>, <a href="/search/quant-ph?searchtype=author&query=Neill%2C+C">Charles Neill</a>, <a href="/search/quant-ph?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/quant-ph?searchtype=author&query=Allen%2C+R">Richard Allen</a>, <a href="/search/quant-ph?searchtype=author&query=Anderson%2C+K">Kyle Anderson</a>, <a href="/search/quant-ph?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/quant-ph?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/quant-ph?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/quant-ph?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/quant-ph?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/quant-ph?searchtype=author&query=Bardin%2C+J">Joseph Bardin</a>, <a href="/search/quant-ph?searchtype=author&query=Bilmes%2C+A">A. Bilmes</a>, <a href="/search/quant-ph?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a> , et al. (156 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.09333v2-abstract-short" style="display: inline;"> Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distributio… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.09333v2-abstract-full').style.display = 'inline'; document.getElementById('2306.09333v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.09333v2-abstract-full" style="display: none;"> Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.09333v2-abstract-full').style.display = 'none'; document.getElementById('2306.09333v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Science 384, 48-53 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.15464">arXiv:2305.15464</a> <span> [<a href="https://arxiv.org/pdf/2305.15464">pdf</a>, <a href="https://arxiv.org/format/2305.15464">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.133.240403">10.1103/PhysRevLett.133.240403 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum turnstiles for robust measurement of full counting statistics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Samajdar%2C+R">Rhine Samajdar</a>, <a href="/search/quant-ph?searchtype=author&query=McCulloch%2C+E">Ewan McCulloch</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Vasseur%2C+R">Romain Vasseur</a>, <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.15464v1-abstract-short" style="display: inline;"> We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures FCS starting from number-indefinite initial states or in the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.15464v1-abstract-full').style.display = 'inline'; document.getElementById('2305.15464v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.15464v1-abstract-full" style="display: none;"> We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures FCS starting from number-indefinite initial states or in the presence of noisy dynamics. In addition, by mapping the FCS onto a single-body observable, it allows for stable numerical calculations of FCS using approximate tensor-network methods. We demonstrate the wide-ranging utility of this approach by computing the FCS of the transferred magnetization in a Floquet Heisenberg spin chain, as studied in a recent experiment with superconducting qubits, as well as the FCS of charge transfer in random circuits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.15464v1-abstract-full').style.display = 'none'; document.getElementById('2305.15464v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8+3 pages, 4+4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 133, 240403 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.11940">arXiv:2305.11940</a> <span> [<a href="https://arxiv.org/pdf/2305.11940">pdf</a>, <a href="https://arxiv.org/format/2305.11940">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevX.14.031014">10.1103/PhysRevX.14.031014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantifying quantum chaos through microcanonical distributions of entanglement </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rodriguez-Nieva%2C+J+F">Joaquin F. Rodriguez-Nieva</a>, <a href="/search/quant-ph?searchtype=author&query=Jonay%2C+C">Cheryne Jonay</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.11940v1-abstract-short" style="display: inline;"> A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this, we introduce a quantitative metric for quantum chaos which utilizes the Kullback-Leibler divergence to compare the microcanonical di… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.11940v1-abstract-full').style.display = 'inline'; document.getElementById('2305.11940v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.11940v1-abstract-full" style="display: none;"> A characteristic feature of "quantum chaotic" systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this, we introduce a quantitative metric for quantum chaos which utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of midspectrum eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). The metric compares not just the averages of the distributions, but also higher moments. The differences in moments are compared on a highly-resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. This distinguishes between chaotic and integrable behavior, and also quantifies the degree of chaos in systems assumed to be chaotic. We study this metric in local minimally structured Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed field Ising model (MFIM). For Hamiltonian systems, the reference random distribution must be constrained to incorporate the effect of energy conservation. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that "maximally chaotic" Hamiltonians may exist in fine-tuned pockets of parameter space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.11940v1-abstract-full').style.display = 'none'; document.getElementById('2305.11940v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16+5 pages, 6+6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. X 14, 031014 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.04792">arXiv:2303.04792</a> <span> [<a href="https://arxiv.org/pdf/2303.04792">pdf</a>, <a href="https://arxiv.org/format/2303.04792">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41586-023-06505-7">10.1038/s41586-023-06505-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Measurement-induced entanglement and teleportation on a noisy quantum processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Hoke%2C+J+C">Jesse C. Hoke</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Rosenberg%2C+E">Eliott Rosenberg</a>, <a href="/search/quant-ph?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/quant-ph?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/quant-ph?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/quant-ph?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/quant-ph?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/quant-ph?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/quant-ph?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/quant-ph?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/quant-ph?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/quant-ph?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/quant-ph?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/quant-ph?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/quant-ph?searchtype=author&query=Bovaird%2C+J">Jenna Bovaird</a>, <a href="/search/quant-ph?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/quant-ph?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/quant-ph?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/quant-ph?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/quant-ph?searchtype=author&query=Burger%2C+T">Tim Burger</a>, <a href="/search/quant-ph?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/quant-ph?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Z">Zijun Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Chiaro%2C+B">Ben Chiaro</a> , et al. (138 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.04792v2-abstract-short" style="display: inline;"> Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.04792v2-abstract-full').style.display = 'inline'; document.getElementById('2303.04792v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.04792v2-abstract-full" style="display: none;"> Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.04792v2-abstract-full').style.display = 'none'; document.getElementById('2303.04792v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature 622, 481-486 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.11963">arXiv:2212.11963</a> <span> [<a href="https://arxiv.org/pdf/2212.11963">pdf</a>, <a href="https://arxiv.org/format/2212.11963">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.130.230403">10.1103/PhysRevLett.130.230403 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Operator relaxation and the optimal depth of classical shadows </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+Y">Yaodong Li</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.11963v3-abstract-short" style="display: inline;"> Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via ``shallow shadows'', a recently-proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of vari… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11963v3-abstract-full').style.display = 'inline'; document.getElementById('2212.11963v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.11963v3-abstract-full" style="display: none;"> Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via ``shallow shadows'', a recently-proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth $t$. We show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (``twirling'') circuit -- namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially-contiguous Pauli operators of weight $k$, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth $t\sim \log(k)$, guarantees an exponential gain in sample complexity over the $t=0$ protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our work connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly-optimized protocols for learning different properties of quantum states. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11963v3-abstract-full').style.display = 'none'; document.getElementById('2212.11963v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">(4+eps pages, 4 figures) main text + (11 pages, 5 figures) supplementary material. v2: switched from state-averaged shadow norm to regular shadow norm, added references. v3: added supplemental section S6 on non-contiguous operators. Accepted version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 130, 230403 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.12526">arXiv:2211.12526</a> <span> [<a href="https://arxiv.org/pdf/2211.12526">pdf</a>, <a href="https://arxiv.org/format/2211.12526">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.109.L020304">10.1103/PhysRevB.109.L020304 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2211.12526v2-abstract-short" style="display: inline;"> Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such systems can undergo dynamical phase transitions in the entanglement properties of quantum trajectories conditional on the measurement outcomes. Here, we explore… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.12526v2-abstract-full').style.display = 'inline'; document.getElementById('2211.12526v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.12526v2-abstract-full" style="display: none;"> Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such systems can undergo dynamical phase transitions in the entanglement properties of quantum trajectories conditional on the measurement outcomes. Here, we explore dynamics in which one attempts to (locally) use those measurement outcomes to steer the system toward a target state, and we study the resulting phase diagram as a function of the measurement and feedback rates. Steering succeeds when the measurement and feedback rates exceed a threshold, yielding an absorbing-state transition in the trajectory-averaged density matrix. We argue that the absorbing-state transition generally occurs at different critical parameters from the entanglement transition in individual trajectories and has distinct critical properties. The efficacy of steering depends on the nature of the target state: in particular, for local dynamics targeting long-range correlated states, steering is necessarily slow and the entanglement and steering transitions are well separated in parameter space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.12526v2-abstract-full').style.display = 'none'; document.getElementById('2211.12526v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2 - published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 109, L020304 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.13444">arXiv:2210.13444</a> <span> [<a href="https://arxiv.org/pdf/2210.13444">pdf</a>, <a href="https://arxiv.org/format/2210.13444">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.108.174303">10.1103/PhysRevB.108.174303 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Universality classes of thermalization for mesoscopic Floquet systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.13444v3-abstract-short" style="display: inline;"> We identify several phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. We also identify a new Floquet thermal ensemble -- the ladder ensemble -- that is qualitatively distinct from the featureless infinite-temperature state that is often assumed to describe the equilibrium of driven systems. The phases can be c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.13444v3-abstract-full').style.display = 'inline'; document.getElementById('2210.13444v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.13444v3-abstract-full" style="display: none;"> We identify several phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. We also identify a new Floquet thermal ensemble -- the ladder ensemble -- that is qualitatively distinct from the featureless infinite-temperature state that is often assumed to describe the equilibrium of driven systems. The phases can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order $蠅$ with the drive, i.e., Floquet thermalizes, and (ii) the ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases represent regimes of behavior in mesoscopic systems, but they are sharply defined in a large-system limit where the drive frequency $蠅$ scales up with system size $N$ as the $N\to\infty$ limit is taken: we examine frequency scalings ranging from a weak $蠅\sim \log N$, to stronger scalings ranging from $蠅\sim \sqrt{N}$ to $蠅\sim N$. We show that the transition where Floquet thermalization breaks down occurs at $蠅\sim N$ and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a separation of scales between $N$ and $蠅$. A striking prediction of our work is that, under perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a novel type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.13444v3-abstract-full').style.display = 'none'; document.getElementById('2210.13444v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 108, 174303 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.13429">arXiv:2210.13429</a> <span> [<a href="https://arxiv.org/pdf/2210.13429">pdf</a>, <a href="https://arxiv.org/format/2210.13429">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Other Condensed Matter">cond-mat.other</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.109.024311">10.1103/PhysRevB.109.024311 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jonay%2C+C">Cheryne Jonay</a>, <a href="/search/quant-ph?searchtype=author&query=Rodriguez-Nieva%2C+J+F">Joaquin F. Rodriguez-Nieva</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.13429v2-abstract-short" style="display: inline;"> Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random $U(1)$ charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin 1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.13429v2-abstract-full').style.display = 'inline'; document.getElementById('2210.13429v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.13429v2-abstract-full" style="display: none;"> Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random $U(1)$ charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin 1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Our results should inform future numerical studies of charge conserving circuits which are relevant for a wide range of topical theoretical questions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.13429v2-abstract-full').style.display = 'none'; document.getElementById('2210.13429v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10+2 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 109, 024311 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.14280">arXiv:2207.14280</a> <span> [<a href="https://arxiv.org/pdf/2207.14280">pdf</a>, <a href="https://arxiv.org/format/2207.14280">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1146/annurev-conmatphys-031720-030658">10.1146/annurev-conmatphys-031720-030658 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Random Quantum Circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Fisher%2C+M+P+A">Matthew P. A. Fisher</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Nahum%2C+A">Adam Nahum</a>, <a href="/search/quant-ph?searchtype=author&query=Vijay%2C+S">Sagar Vijay</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.14280v1-abstract-short" style="display: inline;"> Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, su… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.14280v1-abstract-full').style.display = 'inline'; document.getElementById('2207.14280v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.14280v1-abstract-full" style="display: none;"> Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.14280v1-abstract-full').style.display = 'none'; document.getElementById('2207.14280v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Review article for Annual Review of Condensed Matter Physics; comments welcome</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annual Review of Condensed Matter Physics 14, 335 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.07096">arXiv:2207.07096</a> <span> [<a href="https://arxiv.org/pdf/2207.07096">pdf</a>, <a href="https://arxiv.org/format/2207.07096">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.108.094304">10.1103/PhysRevB.108.094304 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Sriram%2C+A">Adithya Sriram</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.07096v2-abstract-short" style="display: inline;"> We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07096v2-abstract-full').style.display = 'inline'; document.getElementById('2207.07096v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.07096v2-abstract-full" style="display: none;"> We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dominantly measured, we find area-law entangled phases that protect two topological qubits (on a torus) for a time exponential in system size. This generalizes the recently-proposed idea of Floquet codes, where logical qubits are dynamically generated by a time-periodic measurement schedule, to a stochastic setting. When all types of bonds are measured with comparable frequency, we find a critical phase with a logarithmic violation of the area-law, which sharply distinguishes it from its Hamiltonian counterpart. The critical phase has the same set of topological qubits, as diagnosed by the tripartite mutual information, but protects them only for a time polynomial in system size. Furthermore, we observe an unusual behavior for the dynamical purification of mixed states, characterized at late times by the dynamical exponent $z = 1/2$ -- a super-ballistic dynamics made possible by measurements. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07096v2-abstract-full').style.display = 'none'; document.getElementById('2207.07096v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9+4 pages, 7+2 figures. v2: 10+5 pages, 7+4 figures. Added Appendix E, improved figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 108, 094304 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.05761">arXiv:2207.05761</a> <span> [<a href="https://arxiv.org/pdf/2207.05761">pdf</a>, <a href="https://arxiv.org/format/2207.05761">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.131.106301">10.1103/PhysRevLett.131.106301 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Phenomenology of the Prethermal Many-Body Localized Regime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Long%2C+D+M">David M. Long</a>, <a href="/search/quant-ph?searchtype=author&query=Crowley%2C+P+J+D">Philip J. D. Crowley</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Chandran%2C+A">Anushya Chandran</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.05761v2-abstract-short" style="display: inline;"> The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized (MBL) regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-bod… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.05761v2-abstract-full').style.display = 'inline'; document.getElementById('2207.05761v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.05761v2-abstract-full" style="display: none;"> The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized (MBL) regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-body resonances. The model explains the decay timescale of mean autocorrelators, the functional form of the decay - a stretched exponential - and relates the value of the stretch exponent to the broad distribution of resonance timescales. The Jacobi method of matrix diagonalization provides numerical access to this distribution, as well as a conceptual framework for our analysis. The resonance model correctly predicts the stretch exponents for several models in the literature. Successive resonances may also underlie slow thermalization in strongly disordered systems in higher dimensions, or with long-range interactions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.05761v2-abstract-full').style.display = 'none'; document.getElementById('2207.05761v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 3 figures + 9 pages, 9 figures; (v2) additional appendix on the absence of rare region effects, new numerical data for Heisenberg model autocorrelation functions and Floquet model decimated element distributions, other clarifications and corrections</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 131, 106301 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.11528">arXiv:2206.11528</a> <span> [<a href="https://arxiv.org/pdf/2206.11528">pdf</a>, <a href="https://arxiv.org/format/2206.11528">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1146/annurev-conmatphys-031620-101617">10.1146/annurev-conmatphys-031620-101617 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Many-Body Scars: A Quasiparticle Perspective </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Chandran%2C+A">Anushya Chandran</a>, <a href="/search/quant-ph?searchtype=author&query=Iadecola%2C+T">Thomas Iadecola</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Moessner%2C+R">Roderich Moessner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.11528v2-abstract-short" style="display: inline;"> Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well-defined in generic many-body systems due to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles througho… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.11528v2-abstract-full').style.display = 'inline'; document.getElementById('2206.11528v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.11528v2-abstract-full" style="display: none;"> Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well-defined in generic many-body systems due to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual non-equilibrium phenomena including many-body revivals and non-thermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.11528v2-abstract-full').style.display = 'none'; document.getElementById('2206.11528v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages + refs, 2 figures. Small changes from v1. Accepted version for Annual review of Condensed Matter Physics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annual Review of Condensed Matter Physics 14, 443 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2204.06017">arXiv:2204.06017</a> <span> [<a href="https://arxiv.org/pdf/2204.06017">pdf</a>, <a href="https://arxiv.org/format/2204.06017">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.106.144201">10.1103/PhysRevB.106.144201 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Many body localization transition with correlated disorder </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Shi%2C+Z+D">Zhengyan Darius Shi</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Vasseur%2C+R">Romain Vasseur</a>, <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2204.06017v2-abstract-short" style="display: inline;"> We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these flu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.06017v2-abstract-full').style.display = 'inline'; document.getElementById('2204.06017v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2204.06017v2-abstract-full" style="display: none;"> We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ell}$; more generally they scale as $\ell^纬$. We discuss both positively correlated disorder ($1/2 < 纬< 1$) and anticorrelated, or "hyperuniform," disorder ($纬< 1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar \emph{et al.} [Phys. Rev. B 102, 125134, (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.06017v2-abstract-full').style.display = 'none'; document.getElementById('2204.06017v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages, including 9 figures, 1 table, and 3 appendices (additional reference added in v2)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 106, 144201 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.09526">arXiv:2203.09526</a> <span> [<a href="https://arxiv.org/pdf/2203.09526">pdf</a>, <a href="https://arxiv.org/format/2203.09526">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.109.024417">10.1103/PhysRevB.109.024417 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Distinct universality classes of diffusive transport from full counting statistics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a>, <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Vasseur%2C+R">Romain Vasseur</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.09526v3-abstract-short" style="display: inline;"> The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.09526v3-abstract-full').style.display = 'inline'; document.getElementById('2203.09526v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.09526v3-abstract-full" style="display: none;"> The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.09526v3-abstract-full').style.display = 'none'; document.getElementById('2203.09526v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11pp., 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review B 109, 024417 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.08044">arXiv:2111.08044</a> <span> [<a href="https://arxiv.org/pdf/2111.08044">pdf</a>, <a href="https://arxiv.org/format/2111.08044">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.3.020331">10.1103/PRXQuantum.3.020331 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Hauru%2C+M">Markus Hauru</a>, <a href="/search/quant-ph?searchtype=author&query=Beall%2C+J">Jackson Beall</a>, <a href="/search/quant-ph?searchtype=author&query=Ganahl%2C+M">Martin Ganahl</a>, <a href="/search/quant-ph?searchtype=author&query=Lewis%2C+A+G+M">Adam G. M. Lewis</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Vidal%2C+G">Guifre Vidal</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.08044v2-abstract-short" style="display: inline;"> Tensor Processing Units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks, but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper we demonstrate the usage of TPUs for massively parallel, classical simulations of quantum many-body dynamics on long timescales. We apply our methods… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.08044v2-abstract-full').style.display = 'inline'; document.getElementById('2111.08044v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.08044v2-abstract-full" style="display: none;"> Tensor Processing Units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks, but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper we demonstrate the usage of TPUs for massively parallel, classical simulations of quantum many-body dynamics on long timescales. We apply our methods to study the phenomenon of Floquet prethermalization, i.e., exponentially slow heating in quantum spin chains subject to high-frequency periodic driving. We simulate the dynamics of L=34 qubits for over $10^5$ Floquet periods, corresponding to circuits with millions of two-qubit gates. The circuits simulated have no additional symmetries and represent a pure-state evolution in the full $2^L$-dimensional Hilbert space. This is achieved by distributing the computation over 128 TPU cores. On that size TPU cluster, we find speedups in wall-clock runtime of 230x and 15x when compared to reference CPU and single-GPU simulations, respectively, for shorter 30-qubit simulations that can be handled by all three platforms. We study the computational cost of the simulations, as a function of both the number of qubits and the number of TPU cores used, up to our maximum capacity of L=40 qubits, which requires a ``full pod" of 2048 TPU cores with tens of terabytes of memory in total. For these simulations, an 8-TPU-core machine is comparable to a single A100 GPU, and thus the full TPU pod is comparable to a machine with hundreds of GPUs. However, the TPU pod is more energy and cost efficient, and readily accessible (via Google Cloud), unlike such large many-GPU configurations. We also study the accumulation of numerical error as a function of circuit depth in very deep circuits. Our work demonstrates that TPUs can offer significant advantages for state-of-the-art simulations of quantum many-body dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.08044v2-abstract-full').style.display = 'none'; document.getElementById('2111.08044v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 7 figures; v2 contains substantial improvements including GPU simulations</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 3, 020331 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2109.00551">arXiv:2109.00551</a> <span> [<a href="https://arxiv.org/pdf/2109.00551">pdf</a>, <a href="https://arxiv.org/format/2109.00551">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> A comment on "Discrete time crystals: rigidity, criticality, and realizations" </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Moessner%2C+R">Roderich Moessner</a>, <a href="/search/quant-ph?searchtype=author&query=Sondhi%2C+S+L">S. L. Sondhi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2109.00551v1-abstract-short" style="display: inline;"> The Letter by N. Y. Yao et. al. [1,2] presents three models for realizing a many-body localized discrete time-crystal (MBL DTC): a short-ranged model [1], its revised version [2], as well as a long-range model of a trapped ion experiment [1,3]. We show that none of these realize an MBL DTC for the parameter ranges quoted in Refs. [1,2]. The central phase diagrams in [1] therefore cannot be reprodu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.00551v1-abstract-full').style.display = 'inline'; document.getElementById('2109.00551v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2109.00551v1-abstract-full" style="display: none;"> The Letter by N. Y. Yao et. al. [1,2] presents three models for realizing a many-body localized discrete time-crystal (MBL DTC): a short-ranged model [1], its revised version [2], as well as a long-range model of a trapped ion experiment [1,3]. We show that none of these realize an MBL DTC for the parameter ranges quoted in Refs. [1,2]. The central phase diagrams in [1] therefore cannot be reproduced. The models show rapid decay of oscillations from generic initial states, in sharp contrast to the robust period doubling dynamics characteristic of an MBL DTC. Long-lived oscillations from special initial states (such as polarized states) can be understood from the familiar low-temperature physics of a static transverse field Ising model, rather than the nonequilibrium physics of an eigenstate-ordered MBL DTC. Our results on the long-range model also demonstrate, by extension, the absence of an MBL DTC in the trapped ion experiment of Ref. [3]. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.00551v1-abstract-full').style.display = 'none'; document.getElementById('2109.00551v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.13571">arXiv:2107.13571</a> <span> [<a href="https://arxiv.org/pdf/2107.13571">pdf</a>, <a href="https://arxiv.org/format/2107.13571">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41586-021-04257-w">10.1038/s41586-021-04257-w <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of Time-Crystalline Eigenstate Order on a Quantum Processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Quintana%2C+C">Chris Quintana</a>, <a href="/search/quant-ph?searchtype=author&query=Greene%2C+A">Ami Greene</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Z">Zijun Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Gross%2C+J">Jonathan Gross</a>, <a href="/search/quant-ph?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/quant-ph?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/quant-ph?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/quant-ph?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/quant-ph?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/quant-ph?searchtype=author&query=Basso%2C+J">Joao Basso</a>, <a href="/search/quant-ph?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/quant-ph?searchtype=author&query=Bilmes%2C+A">Alexander Bilmes</a>, <a href="/search/quant-ph?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/quant-ph?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/quant-ph?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/quant-ph?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/quant-ph?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/quant-ph?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/quant-ph?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a>, <a href="/search/quant-ph?searchtype=author&query=Chiaro%2C+B">Benjamin Chiaro</a>, <a href="/search/quant-ph?searchtype=author&query=Collins%2C+R">Roberto Collins</a>, <a href="/search/quant-ph?searchtype=author&query=Courtney%2C+W">William Courtney</a>, <a href="/search/quant-ph?searchtype=author&query=Debroy%2C+D">Dripto Debroy</a> , et al. (80 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.13571v2-abstract-short" style="display: inline;"> Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dyn… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.13571v2-abstract-full').style.display = 'inline'; document.getElementById('2107.13571v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.13571v2-abstract-full" style="display: none;"> Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.13571v2-abstract-full').style.display = 'none'; document.getElementById('2107.13571v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature 601, 531 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.05642">arXiv:2107.05642</a> <span> [<a href="https://arxiv.org/pdf/2107.05642">pdf</a>, <a href="https://arxiv.org/format/2107.05642">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.105.174205">10.1103/PhysRevB.105.174205 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Avalanches and many-body resonances in many-body localized systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Colmenarez%2C+L">Luis Colmenarez</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Luitz%2C+D+J">David J. Luitz</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.05642v3-abstract-short" style="display: inline;"> We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some "landmarks" within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.05642v3-abstract-full').style.display = 'inline'; document.getElementById('2107.05642v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.05642v3-abstract-full" style="display: none;"> We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some "landmarks" within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.05642v3-abstract-full').style.display = 'none'; document.getElementById('2107.05642v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages, 17 figures, v2 contains updated avalanche numerics and discussion, v3 contains minor clarifications</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 105, 174205 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.07686">arXiv:2106.07686</a> <span> [<a href="https://arxiv.org/pdf/2106.07686">pdf</a>, <a href="https://arxiv.org/format/2106.07686">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevResearch.3.043046">10.1103/PhysRevResearch.3.043046 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tri-unitary quantum circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jonay%2C+C">Cheryne Jonay</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.07686v2-abstract-short" style="display: inline;"> We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.07686v2-abstract-full').style.display = 'inline'; document.getElementById('2106.07686v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.07686v2-abstract-full" style="display: none;"> We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges, $未x=\pm v未t$, and the static worldline $未x=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes model-dependent. Finally, we extend our circuit construction to $2+1$ dimensions, where two-point correlation functions are confined to the one-dimensional edges of a tetrahedral light cone -- a subdimensional propagation of information reminiscent of "fractonic" physics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.07686v2-abstract-full').style.display = 'none'; document.getElementById('2106.07686v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages main text + 2 page appendix, 15 figures. v2: added references, fixed typos</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Research 3, 043046 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.06873">arXiv:2103.06873</a> <span> [<a href="https://arxiv.org/pdf/2103.06873">pdf</a>, <a href="https://arxiv.org/format/2103.06873">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevX.12.011045">10.1103/PhysRevX.12.011045 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Rakovszky%2C+T">Tibor Rakovszky</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.06873v3-abstract-short" style="display: inline;"> The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich va… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.06873v3-abstract-full').style.display = 'inline'; document.getElementById('2103.06873v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.06873v3-abstract-full" style="display: none;"> The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size -- from logarithmic to extensive to \emph{fractal}. We show how these outcomes in non-unitary circuits (that are "spacetime-dual" to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets "radiated away" from one edge of the system. In spacetime-duals of chaotic unitary circuits, this mapping allows us to uncover a non-thermal volume-law entangled phase with a logarithmic correction to the entropy distinct from other known examples. Most notably, we also find novel steady state phases with \emph{fractal} entanglement scaling, $S(\ell) \sim \ell^伪$ with tunable $0 < 伪< 1$ for subsystems of size $\ell$ in one dimension. These fractally entangled states add a qualitatively new entry to the families of many-body quantum states that have been studied as energy eigenstates or dynamical steady states, whose entropy almost always displays either area-law, volume-law or logarithmic scaling. We also present an experimental protocol for preparing these novel steady states with only a very limited amount of postselection via a type of "teleportation" between spacelike and timelike slices of quantum circuits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.06873v3-abstract-full').style.display = 'none'; document.getElementById('2103.06873v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: updated interpretation of volume-law phase, added discussion on breaking unitarity. v3: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. X 12, 011045 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2010.15840">arXiv:2010.15840</a> <span> [<a href="https://arxiv.org/pdf/2010.15840">pdf</a>, <a href="https://arxiv.org/format/2010.15840">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.126.060501">10.1103/PhysRevLett.126.060501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Postselection-free entanglement dynamics via spacetime duality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2010.15840v2-abstract-short" style="display: inline;"> The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhea… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.15840v2-abstract-full').style.display = 'inline'; document.getElementById('2010.15840v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2010.15840v2-abstract-full" style="display: none;"> The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of \emph{spacetime duality}. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.15840v2-abstract-full').style.display = 'none'; document.getElementById('2010.15840v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages main text + 9 page supplemental material. v2: added references, expanded supplement, minor modifications to text</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 126, 060501 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.09113">arXiv:2008.09113</a> <span> [<a href="https://arxiv.org/pdf/2008.09113">pdf</a>, <a href="https://arxiv.org/format/2008.09113">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Perturbative instability towards delocalization at phase transitions between MBL phases </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Moudgalya%2C+S">Sanjay Moudgalya</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.09113v1-abstract-short" style="display: inline;"> We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet transition in a disordered transverse field Ising model in one dimension. We find evidence for a perturbative instability of localization at finite energy densities once interactions are added, i.e. ev… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.09113v1-abstract-full').style.display = 'inline'; document.getElementById('2008.09113v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.09113v1-abstract-full" style="display: none;"> We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet transition in a disordered transverse field Ising model in one dimension. We find evidence for a perturbative instability of localization at finite energy densities once interactions are added, i.e. evidence for the relevance of interactions - in a renormalization group sense - to the non-interacting critical point governed by infinite randomness scaling. We introduce a novel diagnostic, the "susceptibility of entanglement", which allows us to perturbatively probe the effect of adding interactions on the entanglement properties of eigenstates, and helps us elucidate the resonant processes that can cause thermalization. The susceptibility serves as a much more sensitive probe, and its divergence can detect the perturbative beginnings of an incipient instability even in regimes and system sizes for which conventional diagnostics point towards localization. We expect this new measure to be of independent interest for analyzing the stability of localization in a variety of different settings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.09113v1-abstract-full').style.display = 'none'; document.getElementById('2008.09113v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.02285">arXiv:2008.02285</a> <span> [<a href="https://arxiv.org/pdf/2008.02285">pdf</a>, <a href="https://arxiv.org/format/2008.02285">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.103.L100207">10.1103/PhysRevB.103.L100207 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topological and symmetry-enriched random quantum critical points </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Duque%2C+C+M">Carlos M. Duque</a>, <a href="/search/quant-ph?searchtype=author&query=Hu%2C+H">Hong-Ye Hu</a>, <a href="/search/quant-ph?searchtype=author&query=You%2C+Y">Yi-Zhuang You</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Verresen%2C+R">Ruben Verresen</a>, <a href="/search/quant-ph?searchtype=author&query=Vasseur%2C+R">Romain Vasseur</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.02285v2-abstract-short" style="display: inline;"> We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.02285v2-abstract-full').style.display = 'inline'; document.getElementById('2008.02285v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.02285v2-abstract-full" style="display: none;"> We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.02285v2-abstract-full').style.display = 'none'; document.getElementById('2008.02285v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 December, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4+epsilon pages+supp mat, 2 figures. v2: New discussion of Floquet systems. A new co-author has been added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 103, 100207 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.16207">arXiv:2007.16207</a> <span> [<a href="https://arxiv.org/pdf/2007.16207">pdf</a>, <a href="https://arxiv.org/format/2007.16207">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevResearch.2.043305">10.1103/PhysRevResearch.2.043305 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=O%27Dea%2C+N">Nicholas O'Dea</a>, <a href="/search/quant-ph?searchtype=author&query=Burnell%2C+F">Fiona Burnell</a>, <a href="/search/quant-ph?searchtype=author&query=Chandran%2C+A">Anushya Chandran</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.16207v2-abstract-short" style="display: inline;"> We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.16207v2-abstract-full').style.display = 'inline'; document.getElementById('2007.16207v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.16207v2-abstract-full" style="display: none;"> We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and $q$-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models into our framework. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.16207v2-abstract-full').style.display = 'none'; document.getElementById('2007.16207v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2- published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Research 2, 043305 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.11602">arXiv:2007.11602</a> <span> [<a href="https://arxiv.org/pdf/2007.11602">pdf</a>, <a href="https://arxiv.org/format/2007.11602">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.2.030346">10.1103/PRXQuantum.2.030346 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Many-body physics in the NISQ era: quantum programming a discrete time crystal </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Kechedzhi%2C+K">Kostyantyn Kechedzhi</a>, <a href="/search/quant-ph?searchtype=author&query=Moessner%2C+R">Roderich Moessner</a>, <a href="/search/quant-ph?searchtype=author&query=Sondhi%2C+S+L">S. L. Sondhi</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.11602v3-abstract-short" style="display: inline;"> Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which {\it physical phenomena}, in the domain of quantum statistica… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.11602v3-abstract-full').style.display = 'inline'; document.getElementById('2007.11602v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.11602v3-abstract-full" style="display: none;"> Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which {\it physical phenomena}, in the domain of quantum statistical mechanics, they may realize more readily than traditional experimental platforms. As a particularly well-suited target, we identify discrete time crystals (DTCs), novel non-equilibrium states of matter that break time translation symmetry. These can only be realized in the intrinsically out-of-equilibrium setting of periodically driven quantum systems stabilized by disorder induced many-body localization. While precursors of the DTC have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers to NMR crystals - none have \emph{all} the necessary ingredients for realizing a fully-fledged incarnation of this phase, and for detecting its signature long-range \emph{spatiotemporal order}. We show that a new generation of quantum simulators can be programmed to realize the DTC phase and to experimentally detect its dynamical properties, a task requiring extensive capabilities for programmability, initialization and read-out. Specifically, the architecture of Google's Sycamore processor is a remarkably close match for the task at hand. We also discuss the effects of environmental decoherence, and how they can be distinguished from `internal' decoherence coming from closed-system thermalization dynamics. Already with existing technology and noise levels, we find that DTC spatiotemporal order would be observable over hundreds of periods, with parametric improvements to come as the hardware advances. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.11602v3-abstract-full').style.display = 'none'; document.getElementById('2007.11602v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: added appendices B and C, added Fig.1, expanded discussion. v3: added Fig. 8</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 2, 030346 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.09560">arXiv:2004.09560</a> <span> [<a href="https://arxiv.org/pdf/2004.09560">pdf</a>, <a href="https://arxiv.org/format/2004.09560">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevX.11.011030">10.1103/PhysRevX.11.011030 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Entanglement phase transitions in measurement-only dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Gullans%2C+M+J">Michael J. Gullans</a>, <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.09560v3-abstract-short" style="display: inline;"> Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unita… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09560v3-abstract-full').style.display = 'inline'; document.getElementById('2004.09560v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.09560v3-abstract-full" style="display: none;"> Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the "scrambling" and "un-scrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local ($\gtrsim 3$-body) operators. We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09560v3-abstract-full').style.display = 'none'; document.getElementById('2004.09560v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages + bibliography and appendices, 10 figures. v2: added section on quantum code properties, added references. v3: substantial changes to the structure of the paper, improved clarity</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. X 11, 011030 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.00096">arXiv:2004.00096</a> <span> [<a href="https://arxiv.org/pdf/2004.00096">pdf</a>, <a href="https://arxiv.org/format/2004.00096">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.101.214205">10.1103/PhysRevB.101.214205 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Kinetically constrained freezing transition in a dipole-conserving system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Morningstar%2C+A">Alan Morningstar</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.00096v3-abstract-short" style="display: inline;"> We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusivel… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.00096v3-abstract-full').style.display = 'inline'; document.getElementById('2004.00096v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.00096v3-abstract-full" style="display: none;"> We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.00096v3-abstract-full').style.display = 'none'; document.getElementById('2004.00096v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 7 figures, 1 table; added new Appendix and additional results in v2; added new Appendix and clarified explanations in v3; published in Physical Review B</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 101, 214205 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.11037">arXiv:2001.11037</a> <span> [<a href="https://arxiv.org/pdf/2001.11037">pdf</a>, <a href="https://arxiv.org/format/2001.11037">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions" </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Moessner%2C+R">Roderich Moessner</a>, <a href="/search/quant-ph?searchtype=author&query=Sondhi%2C+S+L">S. L. Sondhi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.11037v1-abstract-short" style="display: inline;"> In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11037v1-abstract-full').style.display = 'inline'; document.getElementById('2001.11037v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.11037v1-abstract-full" style="display: none;"> In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11037v1-abstract-full').style.display = 'none'; document.getElementById('2001.11037v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">1.5 pages; Comment on Phys. Rev. Lett. 123, 210602</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.08226">arXiv:2001.08226</a> <span> [<a href="https://arxiv.org/pdf/2001.08226">pdf</a>, <a href="https://arxiv.org/ps/2001.08226">ps</a>, <a href="https://arxiv.org/format/2001.08226">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevX.10.021044">10.1103/PhysRevX.10.021044 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Floquet prethermalization in a Bose-Hubbard system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Rubio-Abadal%2C+A">Antonio Rubio-Abadal</a>, <a href="/search/quant-ph?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/quant-ph?searchtype=author&query=Hollerith%2C+S">Simon Hollerith</a>, <a href="/search/quant-ph?searchtype=author&query=Wei%2C+D">David Wei</a>, <a href="/search/quant-ph?searchtype=author&query=Rui%2C+J">Jun Rui</a>, <a href="/search/quant-ph?searchtype=author&query=Sondhi%2C+S+L">S. L. Sondhi</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Gross%2C+C">Christian Gross</a>, <a href="/search/quant-ph?searchtype=author&query=Bloch%2C+I">Immanuel Bloch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.08226v2-abstract-short" style="display: inline;"> Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prether… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.08226v2-abstract-full').style.display = 'inline'; document.getElementById('2001.08226v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.08226v2-abstract-full" style="display: none;"> Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.08226v2-abstract-full').style.display = 'none'; document.getElementById('2001.08226v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. X 10, 021044 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.01137">arXiv:1910.01137</a> <span> [<a href="https://arxiv.org/pdf/1910.01137">pdf</a>, <a href="https://arxiv.org/format/1910.01137">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.101.174204">10.1103/PhysRevB.101.174204 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Localization from Hilbert space shattering: from theory to physical realizations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Hermele%2C+M">Michael Hermele</a>, <a href="/search/quant-ph?searchtype=author&query=Nandkishore%2C+R+M">Rahul M. Nandkishore</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1910.01137v2-abstract-short" style="display: inline;"> We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a `fractonic' model of quantum dynamics constrained to conserve both charge and dipole moment… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.01137v2-abstract-full').style.display = 'inline'; document.getElementById('1910.01137v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.01137v2-abstract-full" style="display: none;"> We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a `fractonic' model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in arbitrary spatial dimensions. A large number of the emergent subsectors, exponentially many in system volume, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. While `fractonic' models provide a particularly clean realization, the shattering phenomenon is more general, as we discuss. We also discuss how the key phenomena may be readily observed in near term ultracold atom experiments. In experimental realizations, the conservation laws are approximate rather than exact, so the localization only survives up to a prethermal timescale that we estimate. We comment on the implications of these results for recent predictions of Bloch/Stark many-body localization. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.01137v2-abstract-full').style.display = 'none'; document.getElementById('1910.01137v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2 is the published version, which combines arXiv:1904.04815 and arXiv:1910.01137 into a single publication. Text overlap with arXiv:1904.04815 expected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 101, 174204 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.03988">arXiv:1909.03988</a> <span> [<a href="https://arxiv.org/pdf/1909.03988">pdf</a>, <a href="https://arxiv.org/ps/1909.03988">ps</a>, <a href="https://arxiv.org/format/1909.03988">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.21468/SciPostPhys.9.2.024">10.21468/SciPostPhys.9.2.024 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Asymmetric butterfly velocities in 2-local Hamiltonians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+Y">Yong-Liang Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1909.03988v2-abstract-short" style="display: inline;"> The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.03988v2-abstract-full').style.display = 'inline'; document.getElementById('1909.03988v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.03988v2-abstract-full" style="display: none;"> The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.03988v2-abstract-full').style.display = 'none'; document.getElementById('1909.03988v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SciPost Phys. 9, 024 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.10371">arXiv:1908.10371</a> <span> [<a href="https://arxiv.org/pdf/1908.10371">pdf</a>, <a href="https://arxiv.org/format/1908.10371">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevX.10.021046">10.1103/PhysRevX.10.021046 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Prethermalization without temperature </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Luitz%2C+D+J">David J. Luitz</a>, <a href="/search/quant-ph?searchtype=author&query=Moessner%2C+R">Roderich Moessner</a>, <a href="/search/quant-ph?searchtype=author&query=Sondhi%2C+S+L">S. L. Sondhi</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.10371v2-abstract-short" style="display: inline;"> While a clean driven system generically absorbs energy until it reaches `infinite temperature', it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for non-trivial dynamics, even from initi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.10371v2-abstract-full').style.display = 'inline'; document.getElementById('1908.10371v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.10371v2-abstract-full" style="display: none;"> While a clean driven system generically absorbs energy until it reaches `infinite temperature', it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for non-trivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localised cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al., [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.10371v2-abstract-full').style.display = 'none'; document.getElementById('1908.10371v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2- published version; discussions expanded and clarified</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. X 10, 021046 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.04815">arXiv:1904.04815</a> <span> [<a href="https://arxiv.org/pdf/1904.04815">pdf</a>, <a href="https://arxiv.org/format/1904.04815">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.101.174204">10.1103/PhysRevB.101.174204 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Local constraints can globally shatter Hilbert space: a new route to quantum information protection </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Nandkishore%2C+R">Rahul Nandkishore</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.04815v3-abstract-short" style="display: inline;"> We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.04815v3-abstract-full').style.display = 'inline'; document.getElementById('1904.04815v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.04815v3-abstract-full" style="display: none;"> We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic circuit dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. A large number of the emergent subsectors, exponentially many in the size of the system, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Exponentially large localized subspaces can be proven to exist for any one dimensional fractonic circuit with finite spatial range, and provide a potentially new route for the robust storage of quantum information. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. The shattering of a particular symmetry sector into a distribution of dynamical subsectors with varying sizes leads to the coexistence of high and low entanglement states, i.e. this provides a general mechanism for the production of quantum many body scars. We discuss the detailed pattern of fracturing and its implications. We also discuss other mechanisms for similarly shattering Hilbert space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.04815v3-abstract-full').style.display = 'none'; document.getElementById('1904.04815v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3 - some discussions expanded and clarified</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 101, 174204 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.05589">arXiv:1812.05589</a> <span> [<a href="https://arxiv.org/pdf/1812.05589">pdf</a>, <a href="https://arxiv.org/format/1812.05589">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Asymmetric butterfly velocities in Hamiltonian and circuit models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Stahl%2C+C">Charles Stahl</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.05589v1-abstract-short" style="display: inline;"> The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily la… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.05589v1-abstract-full').style.display = 'inline'; document.getElementById('1812.05589v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.05589v1-abstract-full" style="display: none;"> The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily large using arbitrarily deep quantum circuits. Nevertheless, in almost all examples of local time-independent Hamiltonians that have been examined thus far, this velocity is independent of the direction of information propagation. In this work, we present two models with asymmetric $v_B$. The first is a time-independent Hamiltonian in one dimension with local, 3-site interactions. The second is a class of local unitary circuits, which we call $n$-staircases, where $n$ serves as a tunable parameter interpolating from $n=1$ with symmetric spreading to $n=\infty$ with completely chiral information propagation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.05589v1-abstract-full').style.display = 'none'; document.getElementById('1812.05589v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1809.02126">arXiv:1809.02126</a> <span> [<a href="https://arxiv.org/pdf/1809.02126">pdf</a>, <a href="https://arxiv.org/format/1809.02126">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.98.220303">10.1103/PhysRevB.98.220303 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Gopalakrishnan%2C+S">Sarang Gopalakrishnan</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a>, <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Vasseur%2C+R">Romain Vasseur</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1809.02126v3-abstract-short" style="display: inline;"> We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.02126v3-abstract-full').style.display = 'inline'; document.getElementById('1809.02126v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1809.02126v3-abstract-full" style="display: none;"> We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.02126v3-abstract-full').style.display = 'none'; document.getElementById('1809.02126v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 98, 220303 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.02108">arXiv:1807.02108</a> <span> [<a href="https://arxiv.org/pdf/1807.02108">pdf</a>, <a href="https://arxiv.org/format/1807.02108">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.99.161101">10.1103/PhysRevB.99.161101 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Signatures of integrability in the dynamics of Rydberg-blockaded chains </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Laumann%2C+C+R">Chris R. Laumann</a>, <a href="/search/quant-ph?searchtype=author&query=Chandran%2C+A">Anushya Chandran</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1807.02108v2-abstract-short" style="display: inline;"> A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its enti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.02108v2-abstract-full').style.display = 'inline'; document.getElementById('1807.02108v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.02108v2-abstract-full" style="display: none;"> A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The unconventional quench dynamics in the parent model could signal a novel class of integrable system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.02108v2-abstract-full').style.display = 'none'; document.getElementById('1807.02108v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 99, 161101 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1803.05902">arXiv:1803.05902</a> <span> [<a href="https://arxiv.org/pdf/1803.05902">pdf</a>, <a href="https://arxiv.org/format/1803.05902">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chaotic Dynamics">nlin.CD</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.98.144304">10.1103/PhysRevB.98.144304 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Khemani%2C+V">Vedika Khemani</a>, <a href="/search/quant-ph?searchtype=author&query=Huse%2C+D+A">David A. Huse</a>, <a href="/search/quant-ph?searchtype=author&query=Nahum%2C+A">Adam Nahum</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1803.05902v2-abstract-short" style="display: inline;"> The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially-extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, $位({\bf v})$, which is the growth or decay rate along "rays" at that velocity. We examine the behavior of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.05902v2-abstract-full').style.display = 'inline'; document.getElementById('1803.05902v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1803.05902v2-abstract-full" style="display: none;"> The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially-extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, $位({\bf v})$, which is the growth or decay rate along "rays" at that velocity. We examine the behavior of $位({\bf v})$ for a variety of many-body systems, both chaotic and integrable. The so-called light cone for the spreading of operators is defined by $位({\bf \hat n}v_B({\bf \hat n}))=0$, with a generally direction-dependent "butterfly speed" $v_B({\bf \hat n})$. In spatially local systems, $位(v)$ is negative outside the light cone where it takes the form $位(v) \sim -(v-v_B)^伪$ near $v_b$, with the exponent $伪$ taking on various values over the range of systems we examine. The regime inside the light cone with positive Lyapunov exponents may only exist for classical, semi-classical or large-$N$ systems, but not for "fully quantum" chaotic systems with strong short-range interactions and local Hilbert space dimensions of order one. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.05902v2-abstract-full').style.display = 'none'; document.getElementById('1803.05902v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 March, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. 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