R\'enyi Entropy of Free Compact Boson on Torus

TL;DR

This paper re-evaluates the Rényi entropy of a free compact scalar on a torus, decomposing it into classical and quantum parts, and explores its behavior in various limits, confirming universal relations.

Contribution

It introduces a different monodromy condition for the classical part and analyzes the low temperature and large interval limits of the entropy.

Findings

Classical part includes all saddle point contributions.

Quantum part remains universal across cases.

Universal relation between entanglement and thermal entropy holds.

Abstract

In this paper, we reconsider the single interval R\'enyi entropy of a free compact scalar on a torus. In this case, the contribution to the entropy could be decomposed into classical part and quantum part. The classical part includes the contribution from all the saddle points, while the quantum part is universal. After considering a different monodromy condition from the one in the literature, we re-evaluate the classical part of the R\'enyi entropy. Moreover, we expand the entropy in the low temperature limit and find the leading thermal correction term which is consistent with the universal behavior suggested in arXiv:1403.0578 [hep-th]. Furthermore we investigate the large interval behavior of the entanglement entropy and show that the universal relation between the entanglement entropy and thermal entropy holds in this case.