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arXiv 0808.4094hep-thcond-mat.stat-mechhep-lat
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纠缠熵与扭曲场

Entanglement Entropy and Twist Fields

Michele Caraglio, Ferdinando Gliozzi

摘要:

量子系统的子系统的纠缠熵在副本方法中通过约化密度矩阵的n次幂的迹关于n的解析延拓来表示。这个迹线可以被认为是一个由原系统的n个独立副本组成的系统中一个合适的可观测量的真空期望值。我们用这个属性来数值计算它在一些二维临界系统,在那里它可以与Calabrese和Cardy,谁写的共形场论的扭曲场的关联函数方面的相同数量的结果进行比较。虽然这两个计算完全匹配,即使在有限的系统中,当分析的子系统由一个单一的区间,他们不同意的子系统是由一个以上的连接部分。这种分歧的原因进行了解释。

英文摘要:

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the analyzed subsystem consists of a single interval, they disagree whenever the subsystem is composed of more than one connected part. The reasons of this disagreement are explained.

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