Rényi Entropy of Free Compact Boson on Torus

Abstract

In this paper, we reconsider the single interval Rényi 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 Rényi 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.

16 pages. Improved arguments, added reference

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Cited by in corpus (5)

• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• Subsystem entropy in 2d CFT and KdV ETH
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Monstrous entanglement
• Rényi entropy of single-character CFTs on the torus