Non-Abelian Statistics in a Quantum Antiferromagnet

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.

Figure 1

The 11 interaction terms included in our trial Hamiltonian with the numerically optimized coefficients (see text).

Figure 2

Spectral plot of our trial Hamiltonian in comparison with the energy expectations values for the three (in the infinite system topologically degenerate) Pfaffian ground states at the $\Gamma$ point. The inset shows the overlap of the Pfaffian states with the three lowest states of our Hamiltonian.