How accurately can the microcanonical ensemble describe small isolated quantum systems?

TL;DR

This study numerically examines how well the microcanonical ensemble describes small isolated quantum systems, finding that accuracy improves rapidly with system size due to eigenstate properties.

Contribution

It demonstrates the scaling behavior of microcanonical ensemble accuracy in small quantum systems and links it to eigenstate correlations and thermalization.

Findings

Accuracy scales as 1/D in certain size ranges

Accuracy improves as 1/√D outside that range

Eigenstate properties influence thermalization

Abstract

We numerically investigate quantum quenches of a nonintegrable hard-core Bose-Hubbard model to test the accuracy of the microcanonical ensemble in small isolated quantum systems. We show that, in a certain range of system size, the accuracy increases with the dimension of the Hilbert space $D$ as $1/D$. We ascribe this rapid improvement to the absence of correlations between many-body energy eigenstates as well as to the eigenstate thermalization. Outside of that range, the accuracy is found to scale as $1/\sqrt{D}$ and improves algebraically with the system size.