{"title":"量子多体伤痕与希尔伯特空间碎片:对精确结果的回顾","authors":"Sanjay Moudgalya, B. Bernevig, N. Regnault","doi":"10.1088/1361-6633/ac73a0","DOIUrl":null,"url":null,"abstract":"The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.","PeriodicalId":21110,"journal":{"name":"Reports on Progress in Physics","volume":null,"pages":null},"PeriodicalIF":19.0000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"181","resultStr":"{\"title\":\"Quantum many-body scars and Hilbert space fragmentation: a review of exact results\",\"authors\":\"Sanjay Moudgalya, B. Bernevig, N. Regnault\",\"doi\":\"10.1088/1361-6633/ac73a0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.\",\"PeriodicalId\":21110,\"journal\":{\"name\":\"Reports on Progress in Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":19.0000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"181\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Progress in Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6633/ac73a0\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Progress in Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6633/ac73a0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Quantum many-body scars and Hilbert space fragmentation: a review of exact results
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.
期刊介绍:
Reports on Progress in Physics is a highly selective journal with a mission to publish ground-breaking new research and authoritative invited reviews of the highest quality and significance across all areas of physics and related areas. Articles must be essential reading for specialists, and likely to be of broader multidisciplinary interest with the expectation for long-term scientific impact and influence on the current state and/or future direction of a field.