The Entanglement Entropy of Solvable Lattice Models

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.Comment: 6 pages; connection with boundary entropy of Affleck and Ludwig added in revised version and notation slightly change