Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases

Abstract

We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed manifold. The closed manifold is bipartitioned into two subsystems, one of which has the same topology as $\mathcal{M}$. Specifically, we focus on the case of generalized string-net models and discuss the cases where $\mathcal{M}$ is a disk or a cylinder. When $\mathcal{M}$ has the topology of a cylinder, different combinations of boundary conditions of the cylinder will correspond to different entanglement cuts on the torus. When both boundaries are charge (smooth) boundaries, the entanglement spectrum can be identified with the boundary excitation distribution spectrum at infinite temperature and constant fugacities. Examples of toric code, ${\mathbb{Z}}_N$ theories, and the simple non-abelian case of doubled Fibonacci are demonstrated.

arXiv commentversion 3

References in corpus (51)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• 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
• Entanglement spectrum of a topological phase in one dimension
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Models for gapped boundaries and domain walls
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• Quantum codes on a lattice with boundary
• Condensate induced transitions between topologically ordered phases
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Protected edge modes without symmetry
• Topological boundary conditions in abelian Chern-Simons theory
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Theory of defects in Abelian topological states
• Bulk-Edge Correspondence in the Entanglement Spectra
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• A geometric proof of the equality between entanglement and edge spectra
• Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Boson Condensation in Topologically Ordered Quantum Liquids
• Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
• Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
• Boundary Degeneracy of Topological Order
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Broken quantum symmetry and confinement phases in planar physics
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Gapless edges of 2d topological orders and enriched monoidal categories
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• Fermion Condensation and Gapped Domain Walls in Topological Orders
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings
• Boundary Hamiltonian theory for gapped topological orders
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Characterizing topological order by the information convex
• General Continuum Clockwork
• Nested Topological Order
• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity
• On Quantum Entanglement in Topological Phases on a Torus

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• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary
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• Temporal Entanglement Transitions in the Periodically Driven Ising Chain