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

• URL: http://arxiv.org/abs/2109.00548v2
• Date: Mon, 20 Jun 2022 05:58:46 GMT
• Title: Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Authors: Sanjay Moudgalya, B. Andrei Bernevig, Nicolas Regnault
• Abstract summary: Quantum Many-Body Scars (QMBS) have shown that a weak violation of ergodicity can lead to rich experimental and theoretical physics. We provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems. We also review Hilbert Space Fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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