Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

TL;DR

This paper develops a lattice Hamiltonian framework for non-Abelian Chern-Simons theories with discrete gauge groups, classifies phase factors, and analyzes fluxon braiding, with applications to dihedral groups.

Contribution

It introduces a local Hamiltonian formulation for non-Abelian discrete gauge Chern-Simons theories and classifies their phase factors, advancing understanding of topological quantum models.

Findings

Classified all possible phase factors for the theory.

Constructed gauge-invariant electric field operators.

Analyzed fluxon braiding properties and applied results to dihedral groups.

Abstract

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.