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.

arXiv comment5+11 pages, 4+5 figures

References in corpus (24)

• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Zoo of quantum-topological phases of matter
• Reduced density matrices and entanglement entropy in free lattice models
• Models for gapped boundaries and domain walls
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Protected edge modes without symmetry
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Interferometry of non-Abelian Anyons
• Generalizations and limitations of string-net models
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Universal tripartite entanglement in one-dimensional many-body systems
• Chiral central charge from a single bulk wave function
• Reflected entropy, symmetries and free fermions
• Gapped boundary theories in three dimensions
• Multipartitioning topological phases by vertex states and quantum entanglement
• The Markov gap for geometric reflected entropy

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• 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