Network construction of non-Abelian chiral spin liquids

TL;DR

This paper constructs a family of non-Abelian chiral spin liquids using a network of chiral junctions, revealing their topological properties, anyonic excitations, and potential stability in quantum materials.

Contribution

It introduces a novel network-based construction of non-Abelian chiral spin liquids with explicit topological and anyonic features, especially focusing on the SU(2)$_2$ model.

Findings

SU(2)$_k$ anyons emerge in the network

Quantized spin and thermal Hall conductances observed

SU(2)$_2$ model exhibits Ising anyons and non-Abelian degeneracy

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.