Ground State Degeneracy of Topological Phases on Open Surfaces

Abstract

We relate the ground state degeneracy (GSD) of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase to a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence to the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The GSD resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Wu-Tao (LWT) charge-pumping argument for Abelian fractional quantum Hall states (FQHS) to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a non-trivial cycle can pump a condensate from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.

arXiv comment5+2 pages, 4 figures, 1 table, (almost) the journal version

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Models for gapped boundaries and domain walls
• Condensate induced transitions between topologically ordered phases
• A classification of symmetry enriched topological phases with exactly solvable models
• Protected edge modes without symmetry
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Theory of defects in Abelian topological states
• Interacting Fibonacci anyons in a Rydberg gas
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Classification of Topological Defects in Abelian Topological States
• A theory of topological edges and domain walls
• Broken quantum symmetry and confinement phases in planar physics
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Coherent Transmutation of Electrons into Fractionalized Anyons
• Symmetry Enriched Phases via Pseudo Anyon Condensation
• A Unified Framework of Topological Phases with Symmetry
• Nested Topological Order
• Accessing topological order in fractionalized liquids with gapped edges

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