Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models

TL;DR

This paper investigates the entanglement properties of matrix product states in spin chains, revealing connections to classical integrable models and critical field theories, and providing exact entropy calculations.

Contribution

It establishes a link between the transfer matrix of VBS states and the Temperley-Lieb algebra, enabling exact Renyi entropy computation for alternating bipartitions.

Findings

Renyi entropy maps to an eight vertex model partition function.

For VBS states, entropy is described by a c=1 conformal field theory.

Generalization to SU(n) VBS relates to dimerization transitions.

Abstract

We study the entanglement properties of a class of ground states defined by matrix product states, which are generalizations of the valence bond solid (VBS) state in one dimension. It is shown that the transfer matrix of these states can be related to representations of the Temperley-Lieb algebra, allowing an exact computation of Renyi entropy. For an alternating bipartition, we find that the Renyi entropy can be mapped to an eight vertex model partition function on a rotated lattice. We also show that for the VBS state, the Renyi entropy of the alternating partition is described by a critical field theory with central charge $c=1$. The generalization to $SU(n)$ VBS and its connection with a dimerization transition in the entanglement Hamiltonian is discussed.