Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy

Abstract

In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.

arXiv comment38 pages, 5 figure; Added reference

References in corpus (34)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Topological orders and Edge excitations in FQH states
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Models for gapped boundaries and domain walls
• Condensate induced transitions between topologically ordered phases
• Generalised twisted partition functions
• Protected edge modes without symmetry
• Topological boundary conditions in abelian Chern-Simons theory
• 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
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Topological defects for the free boson CFT
• A theory of topological edges and domain walls
• Symmetry breaking boundaries I. General theory
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Fusion of conformal interfaces
• Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
• Boundary Degeneracy of Topological Order
• Entanglement through conformal interfaces
• Universal features of left-right entanglement entropy
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Broken quantum symmetry and confinement phases in planar physics
• Generalized ADE Classification of Gapped Domain Walls
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• Left-Right Entanglement Entropy of Boundary States
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Entanglement and topological interfaces
• Characterizing topological order by the information convex

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