Entanglement of two blocks of spins in the critical Ising model

TL;DR

This paper analyzes the entanglement entropy between two blocks of spins in a critical Ising model, providing analytical and numerical insights into how entanglement scales with block size and distance at criticality.

Contribution

It derives an explicit formula for the entanglement entropy of two blocks in the critical Ising model, validated by numerical results.

Findings

Entropy is additive when blocks are infinitely separated.

Analytical results for blocks of size 1 and 2 at criticality.

Derived an entropy formula as a function of block size and distance.

Abstract

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and L=2. In the general case, the critical entropy is shown to be additive when d goes to infinity. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d. This formula is in excellent agreement with numerical results.