{"title":"Efficient simulation of low-temperature physics in one-dimensional gapless systems","authors":"Yuya Kusuki, Kotaro Tamaoka, Zixia Wei, Yasushi Yoneta","doi":"10.1103/physrevb.110.l041122","DOIUrl":null,"url":null,"abstract":"We discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>0</mn><mo><</mo><mi>q</mi><mo>≤</mo><mn>1</mn></mrow></math>. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>O</mi><mo>(</mo><mi>c</mi><msup><mi>N</mi><mn>0</mn></msup><mo form=\"prefix\">log</mo><mi>β</mi><mo>)</mo></mrow></math> where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>c</mi></math> is the central charge and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math> is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.l041122","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index . In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as where is the central charge and is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
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