Quantum many-body scars and Hilbert space fragmentation: a review of exact results
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.
Additional Information
© 2022 IOP Publishing Ltd. Received 8 April 2022; Accepted 26 May 2022; Published 1 July 2022. We are particularly grateful to Lesik Motrunich for enlightening discussions. We also acknowledge useful discussions with Berislav Buca, Dumitru Calugaru, Paul Fendley, David Huse, Tom Iadecola, Frank Pollmann, and Pablo Sala. We thank Stephan Rachel, Abhinav Prem, Rahul Nandkishore, Ana Hudomal, Ivana Vasic, Zlatko Papic, Loic Herviou, Jens Bardarson, Edward O'Brien, Paul Fendley, and Lesik Motrunich for previous collaborations on related topics. We are grateful to Yichen Huang, Tom Iadecola, Igor Klebanov, Kiryl Pakrouski, Zlatko Papic, Fedor Popov, Frank Pollmann, Lesik Motrunich, Pablo Sala, and Lenart Zadnik for their comments and feedback on an earlier version of this review. This work is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 101020833). This work is supported by the Walter Burke Institute for Theoretical Physics at Caltech and the Institute for Quantum Information and Matter. SM acknowledges the hospitality of the Aspen Center for Physics, where a part of this work was completed. The Aspen Center for Physics is supported by National Science Foundation Grant PHY-1607611. This work was also partially supported by a Grant from the Simons Foundation. Data availability statement: No new data were created or analysed in this study.Attached Files
Accepted Version - Regnault+et+al_2022_Rep._Prog._Phys._10.1088_1361-6633_ac73a0.pdf
Submitted - 2109.00548.pdf
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Additional details
- Eprint ID
- 112396
- DOI
- 10.1088/1361-6633/ac73a0
- Resolver ID
- CaltechAUTHORS:20211213-225027530
- 101020833
- European Research Council (ERC)
- Walter Burke Institute for Theoretical Physics, Caltech
- Institute for Quantum Information and Matter (IQIM)
- PHY-1607611
- NSF
- Simons Foundation
- Created
-
2021-12-15Created from EPrint's datestamp field
- Updated
-
2022-07-29Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics