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Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results

Moudgalya, Sanjay and Bernevig, B. Andrei and Regnault, Nicolas (2021) Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results. . (Unpublished)

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The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki (AKLT) 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.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Bernevig, B. Andrei0000-0001-6337-4024
Regnault, Nicolas0000-0002-0210-2428
Additional Information: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 Tom Iadecola, Igor Klebanov, Kiryl Pakrouski, Zlatko Papic, Fedor Popov, Frank Pollmann, and Lesik Motrunich for their comments and feedback on a draft 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). S.M. 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.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)101020833
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20211213-225027530
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112396
Deposited By: George Porter
Deposited On:15 Dec 2021 18:46
Last Modified:15 Dec 2021 18:46

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