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.

arXiv comment16 pages. Improved arguments, added reference

References in corpus (19)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• On Geometric Entropy
• Holographic Entanglement Entropy: An Overview
• Entanglement entropy in free quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement Entropy from a Holographic Viewpoint
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Entanglement Entropy of a Massive Fermion on a Torus
• Single Interval Rényi Entropy At Low Temperature
• Renyi entropies of free bosons on the torus and holography
• Area law and vacuum reordering in harmonic networks
• Universal relation between thermal entropy and entanglement entropy in CFT
• Large Interval Limit of Rényi Entropy At High Temperature
• Entanglement entropy and the simulation of Quantum Mechanics

Cited by in corpus (12)

• Large Interval Limit of Rényi Entropy At High Temperature
• Entanglement, Replicas, and Thetas
• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• Two intervals Rényi entanglement entropy of compact free boson on torus
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Subsystem entropy in 2d CFT and KdV ETH
• A perturbative expansion for entanglement entropy in string theory
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Rényi Entropy for the $\sun1$ WZW model on the torus
• Monstrous entanglement
• Free compact boson on branched coverings of the torus
• Rényi entropy of single-character CFTs on the torus