2004/05/31 by Pasquale Calabrese, John Cardy · 21 citations
Physics and Astronomy · #hep-th #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1088/1742-5468/2004/06/p06002
published as J.Stat.Mech.0406:P06002,2004 · 33 pages, 2 figures. Our results for more than one interval are in general incorrect. A note had been added discussing this
arxiv created 2008/10/02 · arxiv updated 2011/02/16
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA=-Tr rhoA log rhoA corresponding to the reduced density matrix rhoA of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result SA∼(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length ξis large but finite, we show that SA∼\cal A(c/6)logξ, where \cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.