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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <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/2408.03105">arXiv:2408.03105</a> <span> [<a href="https://arxiv.org/pdf/2408.03105">pdf</a>, <a href="https://arxiv.org/format/2408.03105">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="Materials Science">cond-mat.mtrl-sci</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</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"> Revealing the Berry phase under the tunneling barrier </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Faeyrman%2C+L">Lior Faeyrman</a>, <a href="/search/cond-mat?searchtype=author&query=Molinero%2C+E+B">Eduardo B. Molinero</a>, <a href="/search/cond-mat?searchtype=author&query=Weiss%2C+R">Roni Weiss</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Kneller%2C+O">Omer Kneller</a>, <a href="/search/cond-mat?searchtype=author&query=Arusi-Parpar%2C+T">Talya Arusi-Parpar</a>, <a href="/search/cond-mat?searchtype=author&query=Bruner%2C+B+D">Barry D. Bruner</a>, <a href="/search/cond-mat?searchtype=author&query=Yan%2C+B">Binghai Yan</a>, <a href="/search/cond-mat?searchtype=author&query=Ivanov%2C+M">Misha Ivanov</a>, <a href="/search/cond-mat?searchtype=author&query=Smirnova%2C+O">Olga Smirnova</a>, <a href="/search/cond-mat?searchtype=author&query=Jimenez-Galan%2C+A">Alvaro Jimenez-Galan</a>, <a href="/search/cond-mat?searchtype=author&query=Piccoli%2C+R">Riccardo Piccoli</a>, <a href="/search/cond-mat?searchtype=author&query=Silva%2C+R+E+F">Rui E. F. Silva</a>, <a href="/search/cond-mat?searchtype=author&query=Dudovich%2C+N">Nirit Dudovich</a>, <a href="/search/cond-mat?searchtype=author&query=Uzan-Narovlansky%2C+A+J">Ayelet J. Uzan-Narovlansky</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="2408.03105v1-abstract-short" style="display: inline;"> In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the Hall effect, orbital magnetism, and polarization. Resolving the quantum nature of these processes commonly requires sensitive quantum techniques, as tunneling, be… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03105v1-abstract-full').style.display = 'inline'; document.getElementById('2408.03105v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.03105v1-abstract-full" style="display: none;"> In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the Hall effect, orbital magnetism, and polarization. Resolving the quantum nature of these processes commonly requires sensitive quantum techniques, as tunneling, being the dominant mechanism in STM microscopy and tunneling transport devices. In this study, we integrate these two phenomena - geometrical phases and tunneling - and observe a complex-valued Berry phase via strong field light matter interactions in condensed matter systems. By manipulating the tunneling barrier, with attoseconds precision, we measure the imaginary Berry phase accumulated as the electron tunnels during a fraction of the optical cycle. Our work opens new theoretical and experimental directions in geometrical phases physics and their realization in condensed matter systems, expanding solid state strong field light metrology to study topological quantum phenomena. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03105v1-abstract-full').style.display = 'none'; document.getElementById('2408.03105v1-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 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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, 4 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/2309.08818">arXiv:2309.08818</a> <span> [<a href="https://arxiv.org/pdf/2309.08818">pdf</a>, <a href="https://arxiv.org/format/2309.08818">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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/10.1007/JHEP08(2024)124">10.1007/JHEP08(2024)124 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A supersymmetric SYK model with a curious low energy behavior </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Biggs%2C+A">Anna Biggs</a>, <a href="/search/cond-mat?searchtype=author&query=Maldacena%2C+J">Juan Maldacena</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</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="2309.08818v1-abstract-short" style="display: inline;"> We consider $\mathcal{N}$ = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like $S = S_{0} + \text{(constant)}T^{a}$, where $a \neq 1$. The large $N$ equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.08818v1-abstract-full').style.display = 'inline'; document.getElementById('2309.08818v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.08818v1-abstract-full" style="display: none;"> We consider $\mathcal{N}$ = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like $S = S_{0} + \text{(constant)}T^{a}$, where $a \neq 1$. The large $N$ equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.08818v1-abstract-full').style.display = 'none'; document.getElementById('2309.08818v1-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 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2301.05732">arXiv:2301.05732</a> <span> [<a href="https://arxiv.org/pdf/2301.05732">pdf</a>, <a href="https://arxiv.org/format/2301.05732">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="Strongly Correlated Electrons">cond-mat.str-el</span> </div> </div> <p class="title is-5 mathjax"> Semiclassical geometry in double-scaled SYK </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Goel%2C+A">Akash Goel</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Verlinde%2C+H">Herman Verlinde</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="2301.05732v1-abstract-short" style="display: inline;"> We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a coupling $位$ in which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK suggests that the correlation functions define a geometry in a two-dimensional bulk, with the 2-point function describing the metric. For small coupling, the fluctuation… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.05732v1-abstract-full').style.display = 'inline'; document.getElementById('2301.05732v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2301.05732v1-abstract-full" style="display: none;"> We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a coupling $位$ in which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK suggests that the correlation functions define a geometry in a two-dimensional bulk, with the 2-point function describing the metric. For small coupling, the fluctuations are highly suppressed, and the bulk describes a rigid (A)dS spacetime. As the coupling increases, the fluctuations become stronger. We study the correction to the curvature of the bulk geometry induced by these fluctuations. We find that as we go deeper into the bulk the curvature increases and that the theory eventually becomes strongly coupled. In general, the curvature is related to energy fluctuations in light operators. We also compute the entanglement entropy of partially entangled thermal states in the semiclassical limit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.05732v1-abstract-full').style.display = 'none'; document.getElementById('2301.05732v1-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, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">27 pages, 7 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/2212.13668">arXiv:2212.13668</a> <span> [<a href="https://arxiv.org/pdf/2212.13668">pdf</a>, <a href="https://arxiv.org/format/2212.13668">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Quantum groups, non-commutative $AdS_2$, and chords in the double-scaled SYK model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Berkooz%2C+M">Micha Berkooz</a>, <a href="/search/cond-mat?searchtype=author&query=Isachenkov%2C+M">Mikhail Isachenkov</a>, <a href="/search/cond-mat?searchtype=author&query=Narayan%2C+P">Prithvi Narayan</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</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="2212.13668v1-abstract-short" style="display: inline;"> We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter $q$, and in the $q\rightarrow 1$ and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a ``boundary particle" on the Euclidean Poincar{茅} disk, which underlies th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.13668v1-abstract-full').style.display = 'inline'; document.getElementById('2212.13668v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.13668v1-abstract-full" style="display: none;"> We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter $q$, and in the $q\rightarrow 1$ and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a ``boundary particle" on the Euclidean Poincar{茅} disk, which underlies the single-sided Schwarzian model. $AdS_2$ carries an action of $\mathfrak{s}\mathfrak{l}(2,{\mathbb R}) \simeq \mathfrak{s}\mathfrak{u}(1,1)$, and we argue that the symmetry of the full DS-SYK model is a certain $q$-deformation of the latter, namely $\mathcal{U}_{\sqrt q}(\mathfrak{s}\mathfrak{u}(1,1))$. We do this by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice deformation of $AdS_2$, which has this $\mathcal{U}_{\sqrt q}(\mathfrak{s}\mathfrak{u}(1,1))$ algebra as its symmetry. We also exhibit the connection to non-commutative geometry of $q$-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of $AdS_3$. There are families of possibly distinct $q$-deformed $AdS_2$ spaces, and we point out which are relevant for the DS-SYK model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.13668v1-abstract-full').style.display = 'none'; document.getElementById('2212.13668v1-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> 27 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">70 pages, 6 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/2211.07029">arXiv:2211.07029</a> <span> [<a href="https://arxiv.org/pdf/2211.07029">pdf</a>, <a href="https://arxiv.org/format/2211.07029">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-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/10.1007/JHEP02(2023)066">10.1007/JHEP02(2023)066 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Klebanov%2C+I+R">Igor R. Klebanov</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Sun%2C+Z">Zimo Sun</a>, <a href="/search/cond-mat?searchtype=author&query=Tarnopolsky%2C+G">Grigory Tarnopolsky</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="2211.07029v3-abstract-short" style="display: inline;"> A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence for its previously proposed Ginzburg-Landau description, which is a $\mathbb{Z}_2$ symmetric theory of two scalar fields with cubic interactions. We also point ou… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.07029v3-abstract-full').style.display = 'inline'; document.getElementById('2211.07029v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.07029v3-abstract-full" style="display: none;"> A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence for its previously proposed Ginzburg-Landau description, which is a $\mathbb{Z}_2$ symmetric theory of two scalar fields with cubic interactions. We also point out that $M(3,8)$ is equivalent to the $(2,8)$ superconformal minimal model with the diagonal modular invariant. Using the 5-loop results for theories of scalar fields with cubic interactions, we exhibit the $6-蔚$ expansions of the dimensions of various operators. Their extrapolations are in quite good agreement with the exact results in 2D. We also use them to approximate the scaling dimensions in $d=3,4,5$ for the theories in the $M(3,8)$ universality class. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.07029v3-abstract-full').style.display = 'none'; document.getElementById('2211.07029v3-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 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 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">24 pages, 2 figures; v3: additional symmetry constraints pointed out, references added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.01847">arXiv:2210.01847</a> <span> [<a href="https://arxiv.org/pdf/2210.01847">pdf</a>, <a href="https://arxiv.org/format/2210.01847">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</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/10.1007/JHEP06(2023)148">10.1007/JHEP06(2023)148 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dualities between fermionic theories and the Potts model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</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="2210.01847v1-abstract-short" style="display: inline;"> We show that a large class of fermionic theories are dual to a $q \to 0$ limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently intro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.01847v1-abstract-full').style.display = 'inline'; document.getElementById('2210.01847v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.01847v1-abstract-full" style="display: none;"> We show that a large class of fermionic theories are dual to a $q \to 0$ limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently introduced family of $OSp(1|2M)$ invariant field theories that provide a UV completion to sigma models with the same symmetry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.01847v1-abstract-full').style.display = 'none'; document.getElementById('2210.01847v1-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 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">19 pages, 6 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/2109.02649">arXiv:2109.02649</a> <span> [<a href="https://arxiv.org/pdf/2109.02649">pdf</a>, <a href="https://arxiv.org/format/2109.02649">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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/10.1007/JHEP02(2022)076">10.1007/JHEP02(2022)076 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Negativity Spectra in Random Tensor Networks and Holography </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Kudler-Flam%2C+J">Jonah Kudler-Flam</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Ryu%2C+S">Shinsei Ryu</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="2109.02649v1-abstract-short" style="display: inline;"> Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and "phase" of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson al… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.02649v1-abstract-full').style.display = 'inline'; document.getElementById('2109.02649v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2109.02649v1-abstract-full" style="display: none;"> Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and "phase" of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions. In holography, these describe the entanglement of fixed-area states. It was found that many fixed-area states have a negativity spectrum given by a semi-circle. More generally, we find new negativity spectra that appear in random tensor networks, as well as in phase transitions in holographic states, wormholes, and holographic states with bulk matter. The smallest random tensor network is the same as a micro-canonical version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world branes. We consider the semi-classical negativity of Hawking radiation and find that contributions from islands should be included. We verify this in the JT gravity model, showing the Euclidean wormhole origin of these contributions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.02649v1-abstract-full').style.display = 'none'; document.getElementById('2109.02649v1-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 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">79 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.00011">arXiv:2108.00011</a> <span> [<a href="https://arxiv.org/pdf/2108.00011">pdf</a>, <a href="https://arxiv.org/format/2108.00011">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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/PRXQuantum.2.040340">10.1103/PRXQuantum.2.040340 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Distinguishing Random and Black Hole Microstates </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Kudler-Flam%2C+J">Jonah Kudler-Flam</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Ryu%2C+S">Shinsei Ryu</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="2108.00011v1-abstract-short" style="display: inline;"> This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603 (2021)], where the relative entropy was used to distinguish random states drawn from the Wishart ensemble as well as black hole microstates. In this work, we expand these ideas by computing many generalizations including the Petz R茅nyi relative entropy, sandwiched R茅nyi relative entropy, fidelities, and trace distances.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.00011v1-abstract-full').style.display = 'inline'; document.getElementById('2108.00011v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.00011v1-abstract-full" style="display: none;"> This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603 (2021)], where the relative entropy was used to distinguish random states drawn from the Wishart ensemble as well as black hole microstates. In this work, we expand these ideas by computing many generalizations including the Petz R茅nyi relative entropy, sandwiched R茅nyi relative entropy, fidelities, and trace distances. These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient. We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks. These phenomena sharpen the relationship between holographic states and random tensor networks. We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation. Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula. We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.00011v1-abstract-full').style.display = 'none'; document.getElementById('2108.00011v1-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> 30 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">57 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.03336">arXiv:2104.03336</a> <span> [<a href="https://arxiv.org/pdf/2104.03336">pdf</a>, <a href="https://arxiv.org/format/2104.03336">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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="Mathematical Physics">math-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/10.1007/JHEP09(2021)196">10.1007/JHEP09(2021)196 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Multi-trace Correlators in the SYK Model and Non-geometric Wormholes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Berkooz%2C+M">Micha Berkooz</a>, <a href="/search/cond-mat?searchtype=author&query=Brukner%2C+N">Nadav Brukner</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Raz%2C+A">Amir Raz</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="2104.03336v2-abstract-short" style="display: inline;"> We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as $N \to \infty$, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connecte… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.03336v2-abstract-full').style.display = 'inline'; document.getElementById('2104.03336v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.03336v2-abstract-full" style="display: none;"> We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as $N \to \infty$, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.03336v2-abstract-full').style.display = 'none'; document.getElementById('2104.03336v2-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 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">81 pages, 23 figures. V2: added short discussion on the modified dip time, and corrected minor typos</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2021, 196 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.13983">arXiv:2006.13983</a> <span> [<a href="https://arxiv.org/pdf/2006.13983">pdf</a>, <a href="https://arxiv.org/format/2006.13983">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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/10.1007/JHEP02(2021)113">10.1007/JHEP02(2021)113 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Complex Sachdev-Ye-Kitaev model in the double scaling limit </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Berkooz%2C+M">Micha Berkooz</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Raj%2C+H">Himanshu Raj</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="2006.13983v2-abstract-short" style="display: inline;"> We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a $U(1)$ global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spect… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.13983v2-abstract-full').style.display = 'inline'; document.getElementById('2006.13983v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.13983v2-abstract-full" style="display: none;"> We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a $U(1)$ global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spectral asymmetry, we consider an analogous asymmetry measure of the 2-point function obeying a non-trivial dependence on the operator's dimension. We also provide the chord diagram structure for an SYK-like model that has a $U(M)$ global symmetry at any disorder realization. We then show how to exactly compute the effect of inserting very heavy operators, with formally infinite conformal dimension. The latter separate the gravitational spacetime into several parts connected by an interface, whose properties are exactly computable at all scales. In particular, light enough states can still go between the spaces. This behavior has a simple description in the chord diagram picture. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.13983v2-abstract-full').style.display = 'none'; document.getElementById('2006.13983v2-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 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">73 pages, 13 figures; v2: references added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.04405">arXiv:2003.04405</a> <span> [<a href="https://arxiv.org/pdf/2003.04405">pdf</a>, <a href="https://arxiv.org/format/2003.04405">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</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/10.1007/JHEP12(2020)110">10.1007/JHEP12(2020)110 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The double scaled limit of Super--Symmetric SYK models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Berkooz%2C+M">Micha Berkooz</a>, <a href="/search/cond-mat?searchtype=author&query=Brukner%2C+N">Nadav Brukner</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Raz%2C+A">Amir Raz</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="2003.04405v1-abstract-short" style="display: inline;"> We compute the exact density of states and 2-point function of the $\mathcal{N} =2$ super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.04405v1-abstract-full').style.display = 'inline'; document.getElementById('2003.04405v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.04405v1-abstract-full" style="display: none;"> We compute the exact density of states and 2-point function of the $\mathcal{N} =2$ super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite $N$, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to $SL_q(2|1)$. For completeness we present an overview of the $\mathcal{N}=1$ super-symmetric SYK model in the large $N$ double-scaled limit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.04405v1-abstract-full').style.display = 'none'; document.getElementById('2003.04405v1-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 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2020, 110 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1811.02584">arXiv:1811.02584</a> <span> [<a href="https://arxiv.org/pdf/1811.02584">pdf</a>, <a href="https://arxiv.org/format/1811.02584">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</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/10.1007/JHEP03(2019)079">10.1007/JHEP03(2019)079 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards a full solution of the large N double-scaled SYK model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Berkooz%2C+M">Micha Berkooz</a>, <a href="/search/cond-mat?searchtype=author&query=Isachenkov%2C+M">Mikhail Isachenkov</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Torrents%2C+G">Genis Torrents</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="1811.02584v2-abstract-short" style="display: inline;"> We compute the exact, all energy scale, 4-point function of the large $N$ double-scaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.02584v2-abstract-full').style.display = 'inline'; document.getElementById('1811.02584v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1811.02584v2-abstract-full" style="display: none;"> We compute the exact, all energy scale, 4-point function of the large $N$ double-scaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of SL$(2)$, that generalizes the Schwarzian to the complete range of energies. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.02584v2-abstract-full').style.display = 'none'; document.getElementById('1811.02584v2-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 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">52+28 pages, 14 figures; v2: references revised, typos corrected, changed normalization of SL(2)_q 6j symbol</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1803.08534">arXiv:1803.08534</a> <span> [<a href="https://arxiv.org/pdf/1803.08534">pdf</a>, <a href="https://arxiv.org/format/1803.08534">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="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/PhysRevD.98.045012">10.1103/PhysRevD.98.045012 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The renormalization group flow in field theories with quenched disorder </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Aharony%2C+O">Ofer Aharony</a>, <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</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="1803.08534v2-abstract-short" style="display: inline;"> In this paper we analyze the renormalization group (RG) flow of field theories with quenched disorder, in which the couplings vary randomly in space. We analyze both classical (Euclidean) disorder and quantum disorder, emphasizing general properties rather than specific cases. The RG flow of the disorder-averaged theories takes place in the space of their coupling constants and also in the space o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08534v2-abstract-full').style.display = 'inline'; document.getElementById('1803.08534v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1803.08534v2-abstract-full" style="display: none;"> In this paper we analyze the renormalization group (RG) flow of field theories with quenched disorder, in which the couplings vary randomly in space. We analyze both classical (Euclidean) disorder and quantum disorder, emphasizing general properties rather than specific cases. The RG flow of the disorder-averaged theories takes place in the space of their coupling constants and also in the space of distributions for the disordered couplings, and the two mix together. We write down a generalization of the Callan-Symanzik equation for the flow of disorder-averaged correlation functions. We find that local operators can mix with the response of the theory to local changes in the disorder distribution, and that the generalized Callan-Symanzik equation mixes the disorder averages of several different correlation functions. For classical disorder we show that this can lead to new types of anomalous dimensions and to logarithmic behavior at fixed points. For quantum disorder we find that the RG flow always generates a rescaling of time relative to space, which at a fixed point generically leads to Lifshitz scaling. The dynamical scaling exponent z behaves as an anomalous dimension (as in other non-relativistic RG flows), and we compute it at leading order in perturbation theory in the disorder for a general theory. Our results agree with a previous perturbative computation by Boyanovsky and Cardy, and with a holographic disorder computation of Hartnoll and Santos. We also find in quantum disorder that local operators mix with non-local (in time) operators under the RG, and that there are critical exponents associated with the disorder distribution that have not previously been discussed. In large N theories the disorder averages may be computed exactly, and we verify that they are consistent with the generalized Callan-Symanzik equations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08534v2-abstract-full').style.display = 'none'; document.getElementById('1803.08534v2-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> 27 March, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 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">62+11 pages, 5 figures. A summary of the results on quantum disorder appears in the companion paper arXiv:1803.08529. v2: references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 98, 045012 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1803.08529">arXiv:1803.08529</a> <span> [<a href="https://arxiv.org/pdf/1803.08529">pdf</a>, <a href="https://arxiv.org/format/1803.08529">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="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.121.071601">10.1103/PhysRevLett.121.071601 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The renormalization group in quantum quenched disorder </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Narovlansky%2C+V">Vladimir Narovlansky</a>, <a href="/search/cond-mat?searchtype=author&query=Aharony%2C+O">Ofer Aharony</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="1803.08529v2-abstract-short" style="display: inline;"> We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and non-local operators. This leads to a new crossover exponent related to the disorder (as in classical disorder). We show that the time coordinate is rescaled at each RG step, lea… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08529v2-abstract-full').style.display = 'inline'; document.getElementById('1803.08529v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1803.08529v2-abstract-full" style="display: none;"> We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and non-local operators. This leads to a new crossover exponent related to the disorder (as in classical disorder). We show that the time coordinate is rescaled at each RG step, leading to Lifshitz scaling at critical points. We write a universal formula for the dynamical scaling exponent z for weak disorder. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08529v2-abstract-full').style.display = 'none'; document.getElementById('1803.08529v2-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> 27 March, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 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">5 pages, 1 figure. A more detailed discussion of the results, together with a discussion of quenched classical disorder, appears in the companion paper arXiv:1803.08534. v2: updated a reference</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 121, 071601 (2018) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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