UC Berkeley

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this Letter we argue 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)=SR(A:B)-I(A:B) between two parties, we argue that for A,B being adjacent subregions in the bulk h=c+3ln2, 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=|C|3ln2 for a Chern-C insulator. Our Letter establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.