Thermal Corrections to R\'enyi entropies for Free Fermions

TL;DR

This paper computes the leading thermal corrections to Rènyi entropies for free massless fermions on a sphere, using conformal mappings and the method of images to evaluate two-point functions on conical geometries.

Contribution

It provides a novel calculation of thermal Rènyi entropy corrections for free fermions on spherical geometries using conformal and image methods.

Findings

Derived explicit formulas for thermal corrections to Rènyi entropies.

Extended previous conformal field theory methods to fermionic systems.

Validated the approach by recovering known results in special cases.

Abstract

We calculate thermal corrections to R\'{e}nyi entropies for free massless fermions on a sphere. More specifically, we take a free fermion on $\mathbb{R}\times\mathbb{S}^{d-1}$ and calculate the leading thermal correction to the R\'{e}nyi entropies for a cap like region with opening angle $2\theta$. By expanding the density matrix in a Boltzmann sum, the problem of finding the R\'{e}nyi entropies can be mapped to the problem of calculating a two point function on an $n$ sheeted cover of the sphere. We follow previous work for conformal field theories to map the problem on the sphere to a conical region in Euclidean space. By using the method of images, we calculate the two point function and recover the R\'{e}nyi entropies.