Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry

TL;DR

This paper investigates how eigenstate thermalization applies to systems with spontaneously broken symmetry, showing that such systems have eigenstates corresponding to different thermal values of order parameters, supported by numerical evidence.

Contribution

It introduces a revised understanding of eigenstate thermalization in systems with broken symmetry, proposing instability towards eigenstates with different thermal order parameter values.

Findings

Eigenstates can correspond to different thermal values of order parameters.

Numerical evidence from 2D transverse-field quantum Ising model supports the theory.

Spontaneous symmetry breaking affects eigenstate thermalization behavior.

Abstract

A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which has multiple thermal values. We propose that in this case the system is unstable towards forming nearby eigenstates which yield each of the allowed thermal values. We provide strong evidence for this from a numerical study of the 2D transverse-field quantum Ising model.