Non-Abelian Statistics in a Quantum Antiferromagnet

TL;DR

This paper introduces a new 2D spin liquid state in a spin-1 antiferromagnet that exhibits non-abelian anyonic excitations, with potential for topological quantum computation.

Contribution

It proposes a novel spin liquid state with non-abelian statistics for spin-1 systems, supported by preliminary numerical evidence and a local Hamiltonian model.

Findings

Deconfined non-abelian spinon and holon excitations

Ground state violates parity and time-reversal symmetry

Potential realization via local three-spin interactions

Abstract

We propose a novel spin liquid state for a spin S=1 antiferromagnet in two dimensions. The ground state violates P and T, is a spin-singlet, and is fully invariant under the lattice symmetries. The spinon and holon excitations are deconfined and obey non-abelian statistics. We present preliminary numerical evidence that the universality class of this topological liquid can be stabilized by a local Hamiltonian involving three-spin interactions. We conjecture that spinons in spin liquids with spin larger than 1/2 obey non-abelian statistics in general.