Entanglement of two blocks of spins in the critical Ising model

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.

published version

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• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
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• Groupoid and algebra of the infinite quantum spin chain
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• A universal approach to Renyi entropy of multiple disjoint intervals