Absence of Thermalization in Nonintegrable Systems

TL;DR

This paper investigates the conditions under which nonintegrable quantum systems fail to thermalize, linking relaxation dynamics to entanglement properties and challenging assumptions about thermalization in such systems.

Contribution

It establishes a connection between relaxation dynamics and entanglement in energy eigenstates, showing that some nonintegrable systems retain memory of initial conditions despite equilibrating.

Findings

Reduced states can equilibrate but retain initial memory.

Equilibrium states are described by maximum entropy or generalized Gibbs ensembles.

Thermalization may not occur even in certain nonintegrable models.

Abstract

We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.