Dynamics and thermalization in correlated one-dimensional lattice systems

TL;DR

This paper reviews how one-dimensional lattice systems of hard-core bosons relax and thermalize after a sudden quench, highlighting the role of integrability and the eigenstate thermalization hypothesis in these processes.

Contribution

It provides a comprehensive analysis of relaxation dynamics in both integrable and nonintegrable 1D lattice systems, emphasizing the transition to thermalization as integrability is broken.

Findings

Integrable systems do not thermalize but can be described by a generalized Gibbs ensemble.

Nonintegrable systems thermalize when sufficiently far from integrability.

Eigenstate thermalization hypothesis explains the onset of thermalization.

Abstract

We review exact approaches and recent results related to the relaxation dynamics and description after relaxation of various one-dimensional lattice systems of hard-core bosons after a sudden quench. We first analyze the integrable case, where the combination of analytical insights and computational techniques enable one to study large system sizes. Thermalization does not occur in this regime. However, after relaxation, observables can be described by a generalization of the Gibbs ensemble. We then utilize full exact diagonalization to study what happens as integrability is broken. We show that thermalization does occur in finite nonintegrable systems provided they are sufficiently far away from the integrable point. We argue that the onset of thermalization can be understood in terms of the eigenstate thermalization hypothesis.