Target space entanglement in quantum mechanics of fermions at finite temperature

TL;DR

This paper explores the behavior of target space entanglement entropy in finite-temperature quantum systems of non-interacting fermions, providing a general formula, numerical analysis, and large N behavior insights.

Contribution

It introduces a general formula for target space Renyi entropy at finite temperature and analyzes its properties through numerical and large N studies.

Findings

Renyi entropy does not follow simple bounds at finite temperature.

Numerical results for a 1D fermion model illustrate entropy behavior.

Large N analysis compares canonical and grand canonical ensembles.

Abstract

We consider the target space entanglement in quantum mechanics of non-interacting fermions at finite temperature. Unlike pure states investigated in arXiv:2105.13726, the (R\'enyi) entanglement entropy for thermal states does not follow a simple bound because all states in the infinite-dimensional Hilbert space are involved. We investigate a general formula of the target space R\'enyi entropy for $N$ fermions at finite temperature, and present numerical results of the entropy in a one-dimensional model. We also argue the large $N$ behaviors with a comparison to the grand canonical ensemble.