The Entanglement Entropy of Solvable Lattice Models

TL;DR

This paper calculates the entanglement entropy of a solvable lattice model, revealing its relation to the central charge and boundary entropy of the associated conformal field theory, thus linking lattice models to continuum CFT descriptions.

Contribution

It extends the understanding of entanglement entropy in solvable lattice models by explicitly relating it to CFT parameters like central charge and boundary entropy.

Findings

Entanglement entropy scales as (c_k/6) ln(xi) plus boundary entropy terms.

The central charge c_k is given by 3k/(k+2) for the model.

The results suggest a general method to connect lattice models with their continuum CFT limits.

Abstract

We consider the spin k/2 analogue of the XXZ quantum spin chain. We compute the entanglement entropy S associated with splitting the infinite chain into two semi-infinite pieces. In the scaling limit, we find S ~ c_k/6 (ln(xi))+ln(g)+... . Here xi is the correlation length and c_k=3k/(k+2) is the central charge associated with the sl_2 WZW model at level k. ln(g) is the boundary entropy of the WZW model. Our result extends previous observations and suggests that this is a simple and perhaps rather general way both of extracting the central charge of the ultraviolet CFT associated with the scaling limit of a solvable lattice model, and of matching lattice and CFT boundary conditions.