On R\'enyi entropies of disjoint intervals in conformal field theory

TL;DR

This paper computes the R\'enyi entropies for multiple disjoint intervals in conformal field theories, specifically the free boson and Ising models, using Riemann surface techniques and verifies results with numerical methods.

Contribution

It provides a novel method to calculate R\'enyi entropies for disjoint intervals in CFTs using Riemann theta functions and confirms these results with numerical simulations.

Findings

Results expressed in terms of Riemann theta functions.

Agreement with numerical simulations for the Ising model.

Validation of the free boson predictions in the decompactification limit.

Abstract

We study the R\'enyi entropies of N disjoint intervals in the conformal field theories given by the free compactified boson and the Ising model. They are computed as the 2N point function of twist fields, by employing the partition function of the model on a particular class of Riemann surfaces. The results are written in terms of Riemann theta functions. The prediction for the free boson in the decompactification regime is checked against exact results for the harmonic chain. For the Ising model, matrix product states computations agree with the conformal field theory result once the finite size corrections have been taken into account.