Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

TL;DR

This study demonstrates that in a nonintegrable system with many local symmetries, the stationary state is better described by a generalized Gibbs ensemble rather than the canonical ensemble, highlighting the importance of local symmetries in thermalization.

Contribution

It shows that the GGE accurately describes stationary states in nonintegrable systems with extensive local symmetries, unlike the canonical ensemble.

Findings

GGE outperforms canonical ensemble in describing stationary states.

Eigenstate thermalization fails globally but holds within symmetry sectors.

Extensive local symmetries necessitate GGE for accurate description.

Abstract

We numerically study the unitary time evolution of a nonintegrable model of hard-core bosons with an extensive number of local Z2 symmetries. We find that the expectation values of local observables in the stationary state are described better by the generalized Gibbs ensemble (GGE) than by the canonical ensemble. We also find that the eigenstate thermalization hypothesis fails for the entire spectrum, but holds true within each symmetry sector, which justifies the GGE. In contrast, if the model has only one global Z2 symmetry or a size-independent number of local Z2 symmetries, we find that the stationary state is described by the canonical ensemble. Thus, the GGE is necessary to describe the stationary state even in a nonintegrable system if it has an extensive number of local symmetries.