Locality and thermalization in closed quantum systems

TL;DR

This paper establishes a new necessary and sufficient condition for thermalization of local observables in closed quantum systems, independent of the eigenstate thermalization hypothesis, and demonstrates its application to finite-size numerical data.

Contribution

It introduces an alternative criterion for thermalization based on local conserved charges, applicable without relying on the eigenstate thermalization hypothesis.

Findings

Local correlators thermalize in the thermodynamic limit.

Eigenstate thermalization hypothesis is not necessary for thermalization.

The new condition can be tested with finite-size numerical data.

Abstract

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as a sum of a projection onto the local conserved charges of the system and a projection onto the non-local ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit although we find no indications that the eigenstate thermalization hypothesis applies.