Entanglement entropy of two disjoint intervals from fusion algebra of twist fields

TL;DR

This paper develops an analytical approximation for the entanglement entropy of two disjoint intervals in conformal field theories using fusion rules of twist fields, validated against exact and numerical results.

Contribution

It introduces a systematic expansion method based on fusion algebra to approximate entanglement entropy in minimal models of CFT.

Findings

Derived an approximate formula for entanglement entropy of disjoint intervals.

Validated the approximation against known exact results.

Confirmed consistency with existing numerical data.

Abstract

We study the entanglement and Renyi entropies of two disjoint intervals in minimal models of conformal field theory. We use the conformal block expansion and fusion rules of twist fields to define a systematic expansion in the elliptic parameter of the trace of the n-th power of the reduced density matrix. Keeping only the first few terms we obtain an approximate expression that is easily analytically continued to n->1, leading to an approximate formula for the entanglement entropy. These predictions are checked against some known exact results as well as against existing numerical data.