Generalized Thermalization in an Integrable Lattice System

TL;DR

This paper introduces a microcanonical generalized Gibbs ensemble (GGE) and explains its success in describing relaxation in integrable systems after a quench, supported by numerical validation in a 1D hard-core boson model.

Contribution

It proposes a microcanonical GGE and a generalized eigenstate thermalization hypothesis to justify thermalization in integrable systems.

Findings

Microcanonical GGE accurately describes post-quench observables.

Numerical validation with up to 10 particles on 50 sites supports the theory.

Generalized eigenstate thermalization explains relaxation in integrable systems.

Abstract

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (~10^10 eigenstates) validate our approach.