Non-Abelian Statistics in a Quantum Antiferromagnet

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.