Entanglement entropy of two disjoint blocks in critical Ising models

TL;DR

This paper investigates how the entanglement entropy of two separate regions in critical Ising models scales with their size and separation, combining conformal field theory with numerical simulations for validation.

Contribution

It provides analytical conformal field theory results for entanglement entropy of disjoint blocks and verifies them through numerical simulations, including finite-size corrections.

Findings

Analytical formulas match numerical data after finite-size correction

Finite length of blocks significantly affects entanglement scaling

Results apply to both quantum and classical Ising models

Abstract

We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively checked in numerical simulations of both the quantum spin chain and the classical two dimensional Ising model. Theoretical results match the ones obtained from numerical simulations only after taking properly into account the corrections induced by the finite length of the blocks to their leading scaling behavior.