Entanglement of a chiral scalar on the torus

TL;DR

This paper calculates the entanglement entropy and Renyi entropies of a chiral scalar field on a torus at any temperature using the resolvent method, providing a comprehensive analysis of quantum entanglement in this system.

Contribution

It introduces a resolvent-based approach to compute entanglement and Renyi entropies for a chiral scalar on a torus, including arbitrary temperatures.

Findings

Derived explicit formulas for entanglement entropy.

Computed all Renyi entropies for the model.

Demonstrated the resolvent method's effectiveness in this context.

Abstract

We compute the entanglement entropy of an interval for a chiral scalar on a circle at an arbitrary temperature. We use the resolvent method, which involves expressing the entropy in terms of the resolvent of a certain operator, and we compute that resolvent by solving a problem that entails finding an analytic function on the complex torus with certain jump conditions at the interval. The resolvent is relevant by itself, since it can be used to compute any function of the reduced density matrix. We illustrate that by also computing all the R\'enyi entropies for the model.