论文标题
反射的熵，对称性和自由费
Reflected entropy, symmetries and free fermions
论文作者
论文摘要
最近，在全息图中提出了量子场理论（QFTS）的分裂特性（QFTS）的概念，这两种概念都在全息环境中提出 - 与纠缠楔形横截面相关 - 与一般QFT有关。我们认为，这种“反映的熵”的定义可以以一种特别适合Orbifold理论的方式进行规范化，这是通过将操作员的完整代数限制为在全球对称组下的中性的。事实证明，这是由全理论反射熵减去与实施对称操作的“扭曲”操作员的期望值相关的熵。然后，我们表明，高斯费米式系统的反射熵可以简单地以相关函数的形式编写，并且在二维迪拉克场（二维迪拉克场）的情况下，我们对其进行了数值评估。最后，我们解释了如何构造上述扭曲操作员，并在$ \ mathbb {z} _2 $ bosonic subgebra的情况下，计算相应的期望值和数值反映熵。
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 $\mathbb{Z}_2$ bosonic subalgebra of the Dirac field.
