A model of chiral spin liquids with Abelian and non-Abelian topological phases

Abstract

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a Random Phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

arXiv comment31 pages, 9 figures

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• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
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• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Exact solution of a anisotropic $J_1-J_2$ spin chain with antiperiodic boundary condition
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
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• Fractional spin excitations and conductance in the spiral staircase Heisenberg ladder
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