Exactly soluble model of boundary degeneracy

Abstract

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

5 pages, 3 figures

References in corpus (12)

• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Dynamical crystallization in a low-dimensional Rydberg gas
• Coherent Excitation Transfer in a Spin Chain of Three Rydberg Atoms
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional Quantum Hall State in Coupled Cavities
• Fractional topological superconductors with fractionalized Majorana fermions
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Fractional Quantum Hall States of Rydberg Polaritons
• Charge $2e/3$ superconductivity and topological degeneracies without localized zero modes in bilayer fractional quantum Hall states
• Modular transformations through sequences of topological charge projections

Cited by in corpus (7)

• Anyon condensation and its applications
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Topological Quantum Computation with Gapped Boundaries
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Topological Quantum Computation with Gapped Boundaries and Boundary Defects