Exactly soluble lattice models for non-Abelian states of matter in two dimensions

Following an earlier construction of exactly soluble lattice models for Abelian fractional topological insulators in two and three dimensions, we construct here an exactly soluble lattice model for a non-Abelian ν=1 quantum Hall state and a non-Abelian topological insulator in two dimensions. We show that both models are topologically ordered, exhibiting fractionalized charge, ground-state degeneracy on the torus, and protected edge modes. The models feature non-Abelian vortices which carry fractional electric charge in the quantum Hall case and spin in the topological insulator case. We analyze the statistical properties of the excitations in detail and discuss the possibility of extending this construction to three-dimensional non-Abelian topological insulators.