Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks

TL;DR

This paper improves the calculation of entanglement entropy for two disjoint intervals in 1+1 dimensional conformal field theories by using conformal block expansion and the Zamolodchikov recursion formula, providing more accurate results.

Contribution

It introduces a method combining conformal block expansion with the Zamolodchikov recursion to enhance entanglement entropy calculations in CFTs, with detailed analysis for specific models.

Findings

Accurate entanglement entropy results obtained by including multiple OPE terms.

Analytic continuation of conformal blocks facilitates von Neumann entropy approximation.

Method successfully applied to Ising CFT and free compactified boson.

Abstract

We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion (OPE) of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy.