Entanglement-ergodic quantum systems equilibrate exponentially well

TL;DR

This paper demonstrates that certain quantum many-body systems with entanglement properties equilibrate exponentially well under unitary evolution, providing new insights into the conditions for equilibration beyond typicality assumptions.

Contribution

It establishes rigorous equilibration results based on entanglement entropy properties of energy eigenstates, linking entanglement to equilibration without relying on typicality.

Findings

Systems with extensive Renyi entanglement entropies in energy eigenstates equilibrate exponentially well.

Results connect entanglement properties to equilibration, offering a new perspective on thermalization.

The work relates to phenomena like many-body localization and many-body scars.

Abstract

One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels. But results not referring to typicality which show that natural initial states actually fulfill this condition are lacking. In this work, we present stringent results for equilibration for systems in which Renyi entanglement entropies in energy eigenstates with finite energy density are extensive for at least some, not necessarily connected, sub-system. Our results reverse the logic of common arguments, in that we derive equilibration from a weak condition akin to the eigenstate thermalization hypothesis, which is usually attributed to thermalization in systems that are assumed to equilibrate in the first place. We put the findings into the context of studies of many-body localization and many-body scars.