Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry

Abstract

We introduce an exactly solvable SU(2) symmetric Kitaev model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 quantum number and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits spin quantum Hall effect with quantized spin Hall conductivity σ^s_{xy}=\hbar/2π, and that the spin response is effectively described the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.

4+epsilon pages, 3 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Power-law spin correlations in a perturbed honeycomb spin model

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