Entanglement entropy of two disjoint intervals in c=1 theories

TL;DR

This paper analytically and numerically investigates the scaling of Renyi entanglement entropy for two disjoint intervals in c=1 conformal field theories, confirming theoretical predictions through simulations of lattice models and quantum spin chains.

Contribution

It provides the first analytic conformal field theory result for the second Renyi entropy of disjoint intervals in a c=1 theory and validates it with extensive numerical simulations.

Findings

Analytic formula for second Renyi entropy in c=1 theories.

Numerical confirmation of conformal field theory predictions.

Effective extrapolation techniques for finite-size corrections.

Abstract

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second order Renyi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor network techniques that allowed to obtain the reduced density matrices of disjoint blocks of the spin-chain and to check the correctness of the predictions for Renyi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks to the leading scaling behavior.