A universal tripartite entanglement signature of ungappable edge states

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.

5+11 pages, 4+5 figures

References in corpus (8)

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• Interferometry of non-Abelian Anyons
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Cited by in corpus (17)

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• Multipartitioning topological phases by vertex states and quantum entanglement
• Reflected entropy is not a correlation measure
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Multipartite entanglement in two-dimensional chiral topological liquids
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Mixed-State Entanglement Measures in Topological Order
• More on symmetry resolved operator entanglement
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
• Fermionic Isometric Tensor Network States in Two Dimensions
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Petz map recovery for long-range entangled quantum many-body states
• Playing nonlocal games with phases of quantum matter
• Finite-Entanglement Scaling of 2D Metals
• Conformal geometry from entanglement
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Geometric additivity of modular commutator for multipartite entanglement