Exactly soluble lattice models for non-abelian states of matter in 2 dimensions

Abstract

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 $\nu =1$ 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 3D non-abelian topological insulators.

References in corpus (2)

• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Topological degeneracy of non-Abelian states for dummies

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• Models of interacting bosons with exact ground states: a unified approach