Edge--Entanglement correspondence for gapped topological phases with symmetry

Abstract

The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study gapped, topologically ordered, non-chiral states with a conserved $U(1)$ charge and show that the entanglement Hamiltonian contains not only the information about topologically distinct edges such phases may admit, but also which of them will be realized in the presence of symmetry breaking/conserving perturbations. We introduce an exactly solvable, charge conserving lattice model of a ${\mathbb{Z}}_2$ spin liquid and derive its edge theory and the entanglement Hamiltonian, also in the presence of perturbations. We construct a field theory of the edge and study its RG flow. We show the precise extent of the correspondence between the information contained in the entanglement Hamiltonian and the edge theory.

arXiv comment14 pages, 4 figures

References in corpus (43)

• Entanglement in quantum critical phenomena
• 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
• Entanglement spectrum of a topological phase in one dimension
• Entanglement renormalization
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• Braiding statistics approach to symmetry-protected topological phases
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Universality of Entropy Scaling in 1D Gap-less Models
• Bosonizing one-dimensional cold atomic gases
• Entanglement spectrum of topological insulators and superconductors
• Quantum codes on a lattice with boundary
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Phases of the one-dimensional Bose-Hubbard model
• A classification of symmetry enriched topological phases with exactly solvable models
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy in fermionic Laughlin states
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Protected edge modes without symmetry
• Classification and analysis of two dimensional abelian fractional topological insulators
• Theory of defects in Abelian topological states
• Fractional topological insulators in three dimensions
• Bulk-Edge Correspondence in the Entanglement Spectra
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Correlated Topological Insulators and the Fractional Magnetoelectric Effect
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Symmetry fractionalization and twist defects
• A geometric proof of the equality between entanglement and edge spectra
• Bipartite entanglement entropy in fractional quantum Hall states
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• How universal is the entanglement spectrum?
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Entanglement spectra of complex paired superfluids
• Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases
• Coherent Transmutation of Electrons into Fractionalized Anyons
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Symmetry protected gapless $Z_2$ spin liquids
• Universal edge information from wave-function deformation

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• An exactly soluble model for a fractionalized Weyl semimetal
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain