Entropy and Temperature in finite isolated quantum systems

TL;DR

This paper compares microcanonical and canonical temperatures in finite isolated quantum systems, analyzing deviations and proposing methods to minimize differences through specific energy window choices.

Contribution

It introduces multiple methods to compute microcanonical entropy and identifies an energy window dependence that reduces temperature deviations.

Findings

Optimal energy window width minimizes temperature deviations

Numerical results show ensemble equivalence improves with specific energy dependence

Different entropy calculation methods are compared for finite quantum systems

Abstract

We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact diagonalization. We thus characterize the deviations from ensemble equivalence at finite sizes. We describe multiple ways to compute the microcanonical entropy and present numerical results for the entropy and temperature computed in these various ways. We show that using an energy window whose width has a particular energy dependence results in a temperature with minimal deviations from the canonical temperature.