A universal tripartite entanglement signature of ungappable edge states

• URL: http://arxiv.org/abs/2110.11965v1
• Date: Fri, 22 Oct 2021 18:00:01 GMT
• Title: A universal tripartite entanglement signature of ungappable edge states
• Authors: Karthik Siva, Yijian Zou, Tomohiro Soejima, Roger S.K. Mong, Michael P. Zaletel
• Abstract summary: Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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