Magnetic domains stabilized by symmetry-protected zero modes

TL;DR

This paper shows that symmetry-protected zero modes in the XX model cause persistent non-ergodic behavior, with a localization transition influenced by coupling and perturbations, revealing stable non-thermal dynamics.

Contribution

It demonstrates how symmetry-protected zero modes induce stable non-ergodic dynamics in quantum systems, with a detailed analysis of localization transition and effects of perturbations.

Findings

Zero modes protect inhomogeneous magnetization for long times.

A localization transition occurs at a critical coupling.

Symmetry-breaking perturbations restore thermalization.

Abstract

Understanding mechanisms for the breakdown of thermalization in closed quantum systems is a central problem in quantum many-body physics. We demonstrate strong non-ergodic behavior in the XX model on coupled chains, where domain-wall initial states retain an inhomogeneous magnetization profile for arbitrarily long times. We find that this effect arises due to exponentially many zero modes protected by chiral symmetry. Using an analysis based on the Lanczos algorithm, we identify a localization transition in the thermodynamic limit at a critical coupling between the chains. We further show that antiferromagnetic defects in the initial state and symmetry-breaking perturbations restore slow thermalization, whereas it remains robust for symmetry-conserving perturbations. These results establish that degenerate, symmetry-protected subspaces can give rise to thermodynamically stable non-ergodic dynamics in experimentally accessible quantum systems.