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

TL;DR

This review explores quantum many-body scars and Hilbert space fragmentation, highlighting exact results, mechanisms, and their implications for weak ergodicity breaking in isolated quantum systems.

Contribution

It provides a comprehensive overview of exact results and unifying frameworks for understanding QMBS and Hilbert space fragmentation in quantum many-body systems.

Findings

Exact revivals occur in systems with equally-spaced towers of states.

QMBS can be understood through simple models like the fermionic Hubbard model.

Hilbert space fragmentation leads to diverse ergodic and non-ergodic behaviors.

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.