Thermalization of exact quantum many-body scars in spin-1 XY chain under perturbation

TL;DR

This paper investigates the stability of quantum many-body scar states in a spin-1 XY chain under perturbations, revealing their eventual thermalization in larger systems and characterizing the decay of associated long-range order and oscillatory dynamics.

Contribution

It provides a finite-size scaling analysis showing scars thermalize in larger chains and estimates the relaxation timescale under perturbation.

Findings

Scar states thermalize in larger chains

Long-range order decays under perturbation

Relaxation timescale scales as λ^{-2}

Abstract

Quantum many-body scars are special eigenstates that violate the eigenstate thermalization hypothesis while residing at finite energy density along with thermalizing eigenstates. The spin-1 XY model is known to host a family of such exceptional states originating from long-lived quasiparticle excitations that exhibit anomalously low entanglement entropy and long-time periodic revivals, resulting in weak ergodicity breaking. We study the stability of these scarred states against typical U(1) symmetry preserving perturbation in the XY chain. While perturbation theory can describe the deformed scar states at small system sizes, finite-size scaling of the perturbation matrix elements indicate that the scars ultimately thermalize in larger chains. Nonetheless, we demonstrate that the long-range order associated with the scars decays under the perturbation, and we estimate the relaxation timescale of oscillatory dynamics in certain local observables to be of order $\lambda^{-2}$, where $\lambda$ is the perturbation strength.