Permutation operators, entanglement entropy, and the XXZ spin chain in the limit \Delta -> -1

TL;DR

This paper introduces a novel method using replica operators to analyze entanglement entropy in integrable quantum spin chains, revealing non-conformal logarithmic scaling in the XXZ model near .

Contribution

It develops a new approach employing replica permutation operators to compute entanglement entropy, connecting lattice models with quantum field theory concepts.

Findings

Entanglement entropy scales logarithmically with system size.

The scaling is non-conformal in the studied limit.

The method links local operators to branch-point twist fields.

Abstract

In this paper we develop a new approach to the investigation of the bi-partite entanglement entropy in integrable quantum spin chains. Our method employs the well-known replica trick, thus taking a replica version of the spin chain model as starting point. At each site i of this new model we construct an operator T_i which acts as a cyclic permutation among the n replicas of the model. Infinite products of T_i give rise to local operators, precursors of branch-point twist fields of quantum field theory. The entanglement entropy is then expressed in terms of correlation functions of such operators. Employing this approach we investigate the von Neumann and R\'enyi entropies of a particularly interesting quantum state occurring as a limit (in a compact convergence topology) of the antiferromagnetic XXZ quantum spin chain. We find that, for large sizes, the entropy scales logarithmically, but not conformally.