Non-Abelian topological phases in an extended Hubbard model

We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a 2D Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons (models A and B) or (spinless) fermions (models C and D). Models A and C also include a ring exchange term. In all four cases we solve equations in the model parameters to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'' $\bar{V}_d$, 0<d<2. Near the ``special'' values, $d = 2 \cos \pi/k+2$, $\bar{V}_d$ should collapse to a stable topological phase with anyonic excitations closely related to SU(2) Chern-Simons theory at level k. We mention simplified models $A^-$ and $C^-$ which may also lead to these topological phases.