2010/11/30 by Olalla A. Castro-Alvaredo, Benjamin Doyon · 41 citations
Computer Science · Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Generalized relative entropy #Integrable system #Joint quantum entropy #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Replica #Thermodynamic limit #Von Neumann entropy #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2011/02/p02001
published in Journal of Statistical Mechanics Theory and Experiment 2011(02), P02001 (Institute of Physics) · 30 pages LaTex, 3 eps figures. V2: small corrections to references. V3: one reference added
arxiv created 2011/01/23 · openalex publication_date 2011/02/01 · arxiv updated 2011/02/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 which acts as a cyclic permutation among the n replicas of the model. Infinite products of 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 Rényi 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.