Exact entanglement entropy of the XYZ model and its sine-Gordon limit

TL;DR

This paper derives the exact entanglement entropy for the XYZ spin chain and its sine-Gordon limit, revealing detailed formulas that connect lattice models to quantum field theory predictions.

Contribution

It provides the first exact expression for the entanglement entropy of the XYZ model and its sine-Gordon limit, linking integrable lattice models with continuum quantum field theories.

Findings

Exact entropy formula for the XYZ model.

Entropy in sine-Gordon limit has a logarithmic plus constant structure.

Results agree with general expectations for massive quantum field theories.

Abstract

We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the 1+1 dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.