Relevance of the eigenstate thermalization hypothesis for thermal relaxation

TL;DR

This paper investigates the eigenstate thermalization hypothesis (ETH) and its significance for thermal relaxation in quantum many-body systems, revealing ETH's validity in nonintegrable systems and its nuanced role in integrable ones.

Contribution

It provides extensive numerical analysis of ETH and thermalization in large quantum spin systems, highlighting differences between integrable and nonintegrable cases.

Findings

ETH becomes valid in the thermodynamic limit for nonintegrable systems.

Nonintegrable systems exhibit initial-state independent equilibration.

Integrable systems show signs of equilibration despite ETH violation.

Abstract

We study the validity of the eigenstate thermalization hypothesis (ETH) and its role for the occurrence of initial-state independent (ISI) equilibration in closed quantum many-body systems. Using the concept of dynamical typicality, we present an extensive numerical analysis of energy exchange in integrable and nonintegrable spin-1/2 systems of large size outside the range of exact diagonalization. In case of nonintegrable systems, our finite-size scaling shows that the ETH becomes valid in the thermodynamic limit and can serve as the underlying mechanism for ISI equilibration. In case of integrable systems, however, indication of ISI equilibration has been observed despite the violation of the ETH. We establish a connection between this observation and the need of choosing a proper parameter within the ETH.