Entanglement Entropy of a Massive Fermion on a Torus

TL;DR

This paper analytically and numerically investigates the entanglement entropies of a massive Dirac fermion on a torus, revealing how mass and temperature influence entropy corrections and their scaling behaviors.

Contribution

It introduces a combined analytical and numerical approach to study entanglement entropy of massive fermions, including small mass corrections via bosonization and lattice computations.

Findings

Corrections to entropies scale as exp(-m/T) in the gapped case.

Analytic and numerical results agree for the entropies.

Non-commuting limits of m to zero and T to zero in ground state degeneracy cases.

Abstract

The Renyi entropies of a massless Dirac fermion on a circle with chemical potential are calculated analytically at nonzero temperature by using the bosonization method. The bosonization of a massive Dirac fermion to the sine-Gordon model lets us obtain the small mass corrections to the entropies. We numerically compute the Renyi entropies by putting a massive fermion on the lattice and find agreement between the analytic and numerical results. In the presence of a mass gap, we show that corrections to Renyi and entanglement entropies in the limit m >> T scale as exp(-m/T). We also show that when there is ground state degeneracy in the gapless case, the limits m to zero and T to zero do not commute.