Slow Thermalization of Exact Quantum Many-Body Scar States Under Perturbations

TL;DR

This paper studies the stability and thermalization dynamics of quantum many-body scar states under perturbations, revealing their slow thermalization and long-lived nonthermal properties in large systems.

Contribution

It provides a theoretical and numerical analysis of how exact scar states evolve under perturbations, including a lower bound on their thermalization time.

Findings

Scar states survive small perturbations at finite sizes

Nonthermal properties persist for long times in quench experiments

Thermalization time scales as λ^{-1/(1+d)} with perturbation strength

Abstract

Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower-bounds the thermalization time for any scar state as $t^{*} \sim O(\lambda^{-1/(1+d)})$, where $d$ is the spatial dimension of the system and $\lambda$ is the perturbation strength.