# Eigenstate thermalization from the clustering property of correlation

## TL;DR

This paper explores how the clustering property of correlations in quantum systems relates to eigenstate thermalization, showing thermalization occurs in low-energy gapped systems and ensemble equivalence in high-energy regimes.

## Contribution

It establishes a connection between the clustering property and eigenstate thermalization, revealing thermalization in low-energy regimes and ensemble equivalence at high energies.

## Key findings

- Eigenstate thermalization occurs in low-energy gapped systems.
- Ensemble equivalence holds in high-energy regimes with small energy shells.
- Clustering property underpins thermalization in non-critical quantum systems.

## Abstract

The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in non-critical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting the clustering property. We investigate two regimes, namely, regimes of high and low density of states corresponding to high and low energy regimes, respectively. We show that the clustering property is connected to several properties on the eigenstate thermalization through the density of states. Remarkably, the eigenstate thermalization is obtained in the low-energy regime with sparse density of states, which is typically seen in gapped systems. For the high-energy regime, we demonstrate the ensemble equivalence between microcanonical and canonical ensembles even for subexponentially small energy shell with respect to the system size, which eventually leads to the weak version of eigenstate thermalization.