Network construction of non-Abelian chiral spin liquids

Abstract

We use a network of chiral junctions to construct a family of topological chiral spin liquids in two spatial dimensions. The chiral spin liquid phase harbors SU(2)${}_k$ anyons, which stem from the underlying SU(2)${}_k$ WZW models that describe the constituent spin chains of the network. The network exhibits quantized spin and thermal Hall conductances. We illustrate our construction by inspecting the topological properties of the SU(2)${}_2$ model. We find that this model has emergent Ising anyons, with spinons acting as vortex excitations that bind Majorana zero modes. We also show that the ground state of this network is threefold degenerate on the torus, asserting its non-Abelian character. Our results shed new light on the stability of non-Abelian topological phases in artificial quantum materials.

arXiv comment24 pages, 4 figures

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• $U(1)$ symmetry-enriched toric code
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Topological ground state degeneracy of the two-channel Kondo lattice
• Majorana Fermi surface state in a network of quantum spin chains