Entanglement entropy and quantum field theory
Entanglement entropy and quantum field theory
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DOI：
10.1088/1742-5468/2004/06/p06002
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发表时间：
2004-06-01
影响因子：
2.4
通讯作者：
Cardy, J
中科院分区：
文献类型：
--
作者：
Calabrese, P;Cardy, J
对相对论量子场论中的纠缠熵进行了系统的研究。这被定义为对应于子系统A的约化密度矩阵rho（A）的冯诺依曼熵S-A = - Trrho（A）log rho（A）。对于1+1维临界系统，其连续极限是中心电荷为c的共形场论，当A是无限系统中长度为l的有限区间时，我们重新导出了类似于Holzhey等人的（c/3）logl的结果S-A，并将其推广到许多其他情况：有限系统，有限温度，以及当A由任意数目的不相交区间组成时.对于这样一个远离其临界点的系统，当相关长度。本文证明了S-A类似于A（c/6）logxi，其中A是A的边界点个数。这些结果被验证的自由质量场理论，这也是用来确认有限大小的非临界系统的情况下，和可积的晶格模型，如伊辛和XXZ模型，这是可解的角转移矩阵方法的标度分析。最后将自由场的结果推广到高维，并用于激发量子相变附近纠缠熵奇异部分的标度形式。
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S-A = - Trrho(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 similar to (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. is large but finite, we show that S-A similar to A(c/6) log 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.