Modular flow as a disentangler
Modular flow as a disentangler
复制标题
DOI：
10.1007/jhep12(2018)083
复制
发表时间：
2018-06
影响因子：
5.4
通讯作者：
Yiming Chen;Xi Dong;Aitor Lewkowycz;X. Qi
中科院分区：
文献类型：
--
作者：
Yiming Chen;Xi Dong;Aitor Lewkowycz;X. Qi
在全息对偶中，边界区域的纠缠熵被认为是与边界区域同源的极值余维2表面的面积的对偶，称为Hubeny-Rangamani-Takayanagi（HRT）表面。本文研究了两个边界子区域R、A的HRT曲面在同一Cauchy切片中的情形。这个条件是必要的子区域-子区域映射是本地的两个子区域和状态有张量网络描述。为了量化这一点，我们研究了一个表面的面积，这是同源的A和极值，除了在可能的交叉点与HRT表面的R（最小化所有这些可能的表面），我们称之为约束面积。我们给出了一个边界建议的上限，这个数量，一个约束是饱和的约束表面相交的HRT表面R在一个恒定的角度。这个边界量是区域A在模演化态中的最小熵，模演化态是与R的模哈密顿量酉演化的状态。我们可以在两个边界维或当模哈密顿量是局部的时候证明这个公式。这个模最小熵是一个边界量，探测大量的因果关系，从这个量，我们可以提取两个HRT表面是在未来还是过去的对方。这些熵满足一些让人想起强次可加性的不等式，并可用于消除某些角点发散。
In holographic duality, the entanglement entropy of a boundary region is proposed to be dual to the area of an extremal codimension-2 surface that is homologous to the boundary region, known as the Hubeny-Rangamani-Takayanagi (HRT) surface. In this paper, we study when the HRT surfaces of two boundary subregions R, A are in the same Cauchy slice. This condition is necessary for the subregion-subregion mapping to be local for both subregions and for states to have a tensor network description. To quantify this, we study the area of a surface that is homologous to A and is extremal except at possible intersections with the HRT surface of R (minimizing over all such possible surfaces), which we call the constrained area. We give a boundary proposal for an upper bound of this quantity, a bound which is saturated when the constrained surface intersects the HRT surface of R at a constant angle. This boundary quantity is the minimum entropy of region A in a modular evolved state—a state that has been evolved unitarily with the modular Hamiltonian of R. We can prove this formula in two boundary dimensions or when the modular Hamiltonian is local. This modular minimal entropy is a boundary quantity that probes bulk causality and, from this quantity, we can extract whether two HRT surfaces are in the future or past of each other. These entropies satisfy some inequalities reminiscent of strong subadditivity and can be used to remove certain corner divergences.