Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-21
J.Stat.Mech.1102:P02001,2011
Physics
High Energy Physics
High Energy Physics - Theory
30 pages LaTex, 3 eps figures. V2: small corrections to references. V3: one reference added
Scientific paper
10.1088/1742-5468/2011/02/P02001
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.
Castro-Alvaredo Olalla A.
Doyon Benjamin
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