Universal tripartite entanglement signature of ungappable edge states
Universal tripartite entanglement signature of ungappable edge states
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DOI：
10.1103/physrevb.106.l041107
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发表时间：
2021-10
影响因子：
3.7
通讯作者：
K. Siva;Yijian Zou;T. Soejima;R. Mong;M. Zaletel
中科院分区：
文献类型：
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作者：
K. Siva;Yijian Zou;T. Soejima;R. Mong;M. Zaletel
有间隙的二维拓扑相可以具有不可间隙的边缘态，即使在没有保护对称性的情况下，这些边缘态也是鲁棒的。在这项工作中，我们展示了最近在全息术背景下提出的多部分纠缠测量，即马尔可夫间隙，提供了不可间隙边缘态的通用诊断。定义为两方之间反射熵和互信息 $h(A:B) = S_R(A:B) - I(A:B)$ 的差异，我们认为，对于 $A,B$ 是块体中相邻的子区域，$h=\frac{c_+}{3}\log 2$，其中 $c_+$ 是边界理论的最小总中心电荷。作为证据，我们证明弦网模型的 $h=0$，并以数值方式验证 Chern-$C$ 绝缘体的 $h=\frac{|C|}{3}\log 2$。我们的工作为边界上共形场论的存在建立了独特的体纠缠标准。
Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this work we show that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information $h(A:B) = S_R(A:B) - I(A:B)$ between two parties, we argue that for $A,B$ being adjacent subregions in the bulk, $h=\frac{c_+}{3}\log 2$, where $c_+$ is the minimal total central charge of the boundary theory. As evidence, we prove that $h=0$ for string-net models, and numerically verify that $h=\frac{|C|}{3}\log 2$ for a Chern-$C$ insulator. Our work establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.