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

TL;DR

This paper constructs exactly soluble lattice models for non-abelian topological phases in 2D, demonstrating fractionalized excitations, ground state degeneracy, and protected edge modes, advancing understanding of non-abelian topological matter.

Contribution

It introduces new exactly soluble lattice models for non-abelian quantum Hall states and topological insulators in two dimensions, extending previous abelian models.

Findings

Models exhibit topological order and fractionalized charge.

Presence of non-abelian vortices with fractional electric charge and spin.

Analysis of excitation statistics and potential 3D extensions.

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.