A universal approach to Renyi entropy of multiple disjoint intervals

TL;DR

This paper introduces a universal method to compute Renyi entropy for multiple disjoint intervals using swapping operations, applicable to quantum field theory and spin models.

Contribution

The authors propose a novel approach linking the replica trick and swapping operations to evaluate Renyi entropy for complex interval configurations.

Findings

Method aligns with conformal field theory results at criticality.

Applicable beyond the critical regime of the Ising model.

Successfully computes Renyi entropy for multiple disjoint intervals.

Abstract

We develop a general theory for computing the Renyi entropy with general multiple disjoint intervals from the swapping operations. Our theory is proposed based on the fact that we have observed the resemblance between the replica trick in quantum field theory and the swapping operation. Consequently, the Renyi entropy can be obtained by evaluating the expectation values of the swapping operator. As an application, we study the Renyi entropy of a one-dimensional transverse-field Ising model for two, three and four disjoint intervals. As the system is at the critical point, our computations of the Renyi entropy are consistent with the analytical results from the conformal field theory. Moreover, our methods can go beyond the critical regime of the Ising model.