Reflected entropy, symmetries and free fermions
Reflected entropy, symmetries and free fermions
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DOI：
10.1007/jhep05(2020)103
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发表时间：
2020-03
影响因子：
5.4
通讯作者：
P. Bueno;H. Casini
中科院分区：
文献类型：
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作者：
P. Bueno;H. Casini
利用量子场论（QFT）的分裂特性，最近提出了一个与空间子区域对相关的冯诺依曼熵的概念，这一概念在全息背景下被认为与纠缠楔横截面有关。我们认为，这个“反射熵”的定义可以规范地推广的方式，这是特别适合于orbifold理论-那些通过限制全代数的运营商是中性的全球对称群。这原来是由全理论反射熵减去与实现对称操作的“扭曲”算子的期望值相关的熵给出的。然后，我们表明，高斯费米子系统的反射熵可以简单地写在相关函数，我们评估它的数值为两个间隔的情况下，二维狄拉克场的共形交比的函数。最后，我们解释了如何可以构造上述扭曲算子，我们计算相应的期望值和反射熵数值的情况下，狄拉克场的bosonic子代数。
Exploiting the split property of quantum field theories (QFTs), a notion of von Neumann entropy associated to pairs of spatial subregions has been recently proposed both in the holographic context—where it has been argued to be related to the entanglement wedge cross section—and for general QFTs. We argue that the definition of this “reflected entropy” can be canonically generalized in a way which is particularly suitable for orbifold theories—those obtained by restricting the full algebra of operators to those which are neutral under a global symmetry group. This turns out to be given by the full-theory reflected entropy minus an entropy associated to the expectation value of the “twist” operator implementing the symmetry operation. Then we show that the reflected entropy for Gaussian fermion systems can be simply written in terms of correlation functions and we evaluate it numerically for two intervals in the case of a two-dimensional Dirac field as a function of the conformal cross-ratio. Finally, we explain how the aforementioned twist operators can be constructed and we compute the corresponding expectation value and reflected entropy numerically in the case of the ℤ 2 bosonic subalgebra of the Dirac field.