Renyi entropy of a free compact boson on a torus

In this paper, we reconsider the single-interval Renyi entropy of a free compact scalar on a torus. In this case, the contribution to the entropy could be decomposed into a classical part and a 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 reevaluate the classical part of the Renyi 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 [J. Cardy and C. P. Herzog, Phys. Rev. Lett. 112, 171603 (2014)]. 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.NSFC [11275010, 11335012, 11325522]SCI(E)ARTICLEbchen01@pku.edu.cn; jieqiangwu@pku.edu.cn109