  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.

Quantum Physics