Permutation operators, entanglement entropy, and theXXZ spin chain in the limit

Abstract

In this paper we develop a new approach to the investigation of the bi-partite entanglemententropy in integrable quantum spin chains. Our method employs the well-known replicatrick, thus taking a replica version of the spin chain model as starting point. At each sitei of this new model we construct an operator which acts as a cyclic permutation among then replicas of the model. Infinite products of give rise to local operators, precursors of branch-point twist fields of quantumfield theory. The entanglement entropy is then expressed in terms of correlationfunctions of such operators. Employing this approach we investigate thevon Neumann and Rényi entropies of a particularly interesting quantum stateoccurring as a limit (in a compact convergence topology) of the antiferromagneticXXZ quantum spin chain. We find that, for large sizes, the entropy scales logarithmically, butnot conformally.