%0 Journal Article %1 Calabrese2008Entanglement %A Calabrese, Pasquale %A Cardy, John %D 2008 %J Journal of Statistical Mechanics: Theory and Experiment %K 2d-cft, entanglement %N 06 %P P06002+ %R 10.1088/1742-5468/2004/06/p06002 %T Entanglement Entropy and Quantum Field Theory %U http://dx.doi.org/10.1088/1742-5468/2004/06/p06002 %V 2004 %X We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S\_A=-Tr rho\_A log rho\_A corresponding to the reduced density matrix rho\_A 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 S\_A\sim(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 \xi is large but finite, we show that S\_AA(c/6)łog\xi, where 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.

@article{Calabrese2008Entanglement, abstract = {We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S\_A=-Tr rho\_A log rho\_A corresponding to the reduced density matrix rho\_A 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 S\_A\sim(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 \xi is large but finite, we show that S\_A\sim{\cal A}(c/6)\log\xi, 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.}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Calabrese, Pasquale and Cardy, John}, biburl = {https://www.bibsonomy.org/bibtex/25fb3d0fd4003d7dfdbb09d23ed4341c2/acastro}, citeulike-article-id = {8977393}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-th/0405152}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-th/0405152}, citeulike-linkout-2 = {http://dx.doi.org/10.1088/1742-5468/2004/06/p06002}, citeulike-linkout-3 = {http://iopscience.iop.org/1742-5468/2004/06/P06002}, day = 2, doi = {10.1088/1742-5468/2004/06/p06002}, eprint = {hep-th/0405152}, interhash = {45a2d207bbbaa56d866964a30283f6c5}, intrahash = {5fb3d0fd4003d7dfdbb09d23ed4341c2}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, keywords = {2d-cft, entanglement}, month = oct, number = 06, pages = {P06002+}, posted-at = {2013-01-16 15:30:39}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Entanglement Entropy and Quantum Field Theory}}, url = {http://dx.doi.org/10.1088/1742-5468/2004/06/p06002}, volume = 2004, year = 2008 }