Ground state degeneracy of non-Abelian topological phases from coupled wires

Abstract

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic $su(2{)}_2^{}$ Moore-Read state, but the approach we outline here can be extended to general bosonic $su(2{)}_k^{}$ topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.

33 pages, 3 figures. v3 replaces previous discussion of 3D case with an outlook. Published version

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• Non-diagonal anisotropic quantum Hall states
• Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Non-Abelian Fusion, Shrinking and Quantum Dimensions of Abelian Gauge Fluxes
• Ground-state properties of electron-electron biwire systems
• Network construction of non-Abelian chiral spin liquids
• Intermediate symmetric construction of transformation between anyon and Gentile statistics
• $U(1)$ symmetry-enriched toric code
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Dihedral twist liquid models from emergent Majorana fermions
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Majorana Fermi surface state in a network of quantum spin chains
• Topological ground state degeneracy of the two-channel Kondo lattice
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays