Lack of thermalization for integrability-breaking impurities

TL;DR

This paper demonstrates that localized integrability-breaking impurities do not lead to thermalization in large times, contrasting with homogeneous perturbations, with analytic results for free bulk systems and interacting impurities.

Contribution

It provides a detailed analysis showing localized impurities do not thermalize systems, unlike homogeneous integrability-breaking terms, with explicit analytic results for specific models.

Findings

Localized impurities do not cause thermalization at large times.

Homogeneous integrability-breaking terms lead to prethermalization and eventual thermalization.

Analytic solutions are derived for free bulk Hamiltonians with interacting impurities.

Abstract

We investigate the effects of localized integrability-breaking perturbations on the large times dynamics of thermodynamic quantum and classical systems. In particular, we suddenly activate an impurity which breaks the integrability of an otherwise homogeneous system. We focus on the large times dynamics and on the thermalization properties of the impurity, which is shown to have mere perturbative effects even at infinite times, thus preventing thermalization. This is in clear contrast with homogeneous integrability-breaking terms, which display the prethermalization paradigm and are expected to eventually cause thermalization, no matter the weakness of the integrability-breaking term. Analytic quantitative results are obtained in the case where the bulk Hamiltonian is free and the impurity interacting.