Quantum many-body scars as remnants of stable many-body periodic orbits

TL;DR

This paper investigates quantum many-body scars (QMBS), revealing they do not correspond to classical periodic orbits and exhibit robustness against perturbations, challenging previous conjectures about their classical chaos connection.

Contribution

The study provides a counterexample showing QMBS are not linked to classical unstable periodic orbits, and demonstrates their robustness even when scarred eigenstates are removed.

Findings

QMBS do not exhibit chaotic behavior in the semiclassical limit.

Anomalous OTOC dynamics persist despite weak perturbations.

Chaotic dynamics are associated with states not related to QMBS.

Abstract

Quantum many-body scars (QMBS) represent a weak ergodicity-breaking phenomenon that defies the common scenario of thermalization in closed quantum systems. They are often regarded as a many-body analog of quantum scars (QS) -- a single-particle phenomenon in quantum chaos -- due to their superficial similarities. However, unlike QS, a clear connection between QMBS and classical chaos has remained elusive. It has nevertheless been speculated that in an appropriate semiclassical limit, QMBS should have a correspondence to weakly unstable periodic orbits. In this paper, I present a counterexample to this conjecture by studying a bosonic model with a large number of flavors. The dynamics of out-of-time-ordered correlators (OTOCs) suggest that QMBS do not display chaotic behavior in the semiclassical limit. In contrast, chaotic dynamics are expected for initial states not associated with QMBS. Interestingly, the anomalous OTOC dynamics persist even under weak perturbations that eliminate the scarred eigenstates, suggesting a certain robustness in the phenomenon.