Realizing non-Abelian statistics

TL;DR

This paper constructs 2+1D models with quasiparticles exhibiting non-Abelian statistics, linking braid matrices to scattering matrices, and explores phase transitions including quantum critical points.

Contribution

It introduces models where quasiparticles obey non-Abelian statistics, connecting braid and scattering matrices, and analyzes phase transitions in these systems.

Findings

Models exhibit non-Abelian anyons with SO(3) Chern-Simons braiding

Ground states relate to Potts model loop representations

Identifies quantum critical points between topological and ordered phases

Abstract

We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of 1+1-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical two-dimensional Potts model. We discuss the transition from a topological phase to a conventionally-ordered phase, showing in some cases there is a quantum critical point.