Entanglement entropy of two disjoint intervals in conformal field theory II

TL;DR

This paper advances the understanding of entanglement entropy in conformal field theories by deriving explicit formulas for two disjoint intervals, validating them against numerical data, and providing systematic asymptotic expansions.

Contribution

It introduces a systematic method for calculating the entanglement entropy of two disjoint intervals in conformal field theories, including explicit formulas and asymptotic expansions.

Findings

Derived explicit formulas for entanglement entropy in the Ising universality class.

Validated predictions against existing numerical data.

Provided analytic continuation of the asymptotic expansion.

Abstract

We continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in J. Stat. Mech. (2009) P11001. We compute Tr\rho_A^n for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann-Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form.