Entanglement entropy of two disjoint intervals in conformal field theory

TL;DR

This paper calculates the entanglement entropy of two disjoint intervals in a Luttinger liquid conformal field theory using twist fields and Riemann-Siegel theta functions, providing analytic results and numerical validation.

Contribution

It introduces a novel analytic method to compute entanglement entropy for disjoint intervals in conformal field theory using twist fields and theta functions.

Findings

Derived a compact formula for ^n in terms of Riemann-Siegel theta functions.

Provided an analytic continuation for all model parameters in the decompactification limit.

Validated predictions against existing numerical data.

Abstract

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.