Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems

TL;DR

This paper investigates how symmetries, integrability, and localization influence thermalization in finite one-dimensional quantum systems, using exact diagonalization to analyze chaos indicators and eigenstate properties.

Contribution

It reveals how symmetry mixing affects chaos indicators and confirms the eigenstate thermalization hypothesis in the chaotic regime of these systems.

Findings

Symmetry mixing impacts chaos indicators derived from eigenvectors.

Eigenstate complexity and observable expectations support thermalization in chaos.

Off-diagonal matrix elements relate to transitions from integrability to chaos and localization.

Abstract

We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest neighbor hopping and interaction, and next-nearest neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.