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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/2204.08777">arXiv:2204.08777</a> <span> [<a href="https://arxiv.org/pdf/2204.08777">pdf</a>, <a href="https://arxiv.org/format/2204.08777">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="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/10.1016/B978-0-323-90800-9.00095-0">10.1016/B978-0-323-90800-9.00095-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Sign Problem in Quantum Monte Carlo Simulation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Pan%2C+G">Gaopei Pan</a>, <a href="/search/hep-lat?searchtype=author&query=Meng%2C+Z+Y">Zi Yang Meng</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="2204.08777v2-abstract-short" style="display: inline;"> Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation techniques, ranging from the world-line and stochastic series expansion Monte Carlo for boson and spin systems to the determinant and momentum-space quantum Monte… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.08777v2-abstract-full').style.display = 'inline'; document.getElementById('2204.08777v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2204.08777v2-abstract-full" style="display: none;"> Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation techniques, ranging from the world-line and stochastic series expansion Monte Carlo for boson and spin systems to the determinant and momentum-space quantum Monte Carlo for interacting fermions. We point out the basis dependency of the sign problem and summarize the progresses to cure, ease and even make use of the sign problem over the years, such as symmetry analysis of the underlying Hamiltonian, basis optimization in writting down the partition functions and many others. Moreover, we state that although traditional lore saying that in case of sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space, there are recent breakthroughs showing this is not always the case and based on the properties of the partition function for finite size systems, one could distinguish when the average sign has the usual exponential scaling and when it is bestowed with an algebraic scaling at the low temperature limit. Fermionic QMC simulations with such algebraic sign problems have been successfully carried out for extended Hubbard-type and quantum Moir茅 lattice models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.08777v2-abstract-full').style.display = 'none'; document.getElementById('2204.08777v2-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 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 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">Book chapter for Elsevier Encyclopedia of Condensed Matter Physics. Comments and missing references are welcome</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> The Encyclopedia of Condensed Matter Physics, 2nd edition, Volume 1, Pages 879-893 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.06139">arXiv:2112.06139</a> <span> [<a href="https://arxiv.org/pdf/2112.06139">pdf</a>, <a href="https://arxiv.org/format/2112.06139">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="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> <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/PhysRevB.106.035121">10.1103/PhysRevB.106.035121 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fermion sign bounds theory in quantum Monte Carlo simulation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+X">Xu Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Pan%2C+G">Gaopei Pan</a>, <a href="/search/hep-lat?searchtype=author&query=Xu%2C+X+Y">Xiao Yan Xu</a>, <a href="/search/hep-lat?searchtype=author&query=Meng%2C+Z+Y">Zi Yang Meng</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="2112.06139v2-abstract-short" style="display: inline;"> Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find phy… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.06139v2-abstract-full').style.display = 'inline'; document.getElementById('2112.06139v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.06139v2-abstract-full" style="display: none;"> Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of reference system and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling at low temperature limit. We analytically explain such algebraic sign problems found in flat band moir茅 lattice models at low temperature limit. At finite temperature, a domain size argument based on sign bounds also explains the connection between sign behavior and finite temperature phase transition. Sign bounds, as a well-defined observable, may have ability to ease or even make use of the sign problem. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.06139v2-abstract-full').style.display = 'none'; document.getElementById('2112.06139v2-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 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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, 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/1912.08229">arXiv:1912.08229</a> <span> [<a href="https://arxiv.org/pdf/1912.08229">pdf</a>, <a href="https://arxiv.org/format/1912.08229">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="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/10.1088/1674-1056/ac4f52">10.1088/1674-1056/ac4f52 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Solving quantum rotor model with different Monte Carlo techniques </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jiang%2C+W">Weilun Jiang</a>, <a href="/search/hep-lat?searchtype=author&query=Pan%2C+G">Gaopei Pan</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+Y">Yuzhi Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Meng%2C+Z+Y">Zi Yang Meng</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="1912.08229v4-abstract-short" style="display: inline;"> We systematically test the performance of several Monte Carlo update schemes for the $(2+1)$d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) scheme, it is clear that among the five different update schemes, at the quantum critical point,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.08229v4-abstract-full').style.display = 'inline'; document.getElementById('1912.08229v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.08229v4-abstract-full" style="display: none;"> We systematically test the performance of several Monte Carlo update schemes for the $(2+1)$d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) scheme, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z$_2$ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.08229v4-abstract-full').style.display = 'none'; document.getElementById('1912.08229v4-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 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">12 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Chin. Phys. 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