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

2005/08/26 by B. Doucot, B Douçot, L. B. Ioffe +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Dihedral group #Gauge (firearms) #Gauge group #Gauge theory #Hamiltonian (control theory) #Hamiltonian lattice gauge theory #Lattice (music) #Lattice gauge theory #Nonlinear Photonic Systems #Topological Materials and Phenomena #cond-mat.stat-mech #cond-mat.supr-con

paper · pdf · doi:10.1088/1367-2630/7/1/187

published as New J.Phys. 7 (2005) 187 · 16 pages, 7 figures

openalex publication_date 2005/08/26 · arxiv created 2005/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation
• Quantum field theory and the Jones polynomial
• Topologically protected quantum bits using Josephson junction arrays
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
• Topological quantum memory
• Fault-tolerant quantum computation by anyons
• Chern-Simons Theory with Finite Gauge Group
• Anyons from nonsolvable finite groups are sufficient for universal quantum computation
• Quantum computing