SU($N$) Toric Code and Nonabelian Anyons
Abstract
We construct SU($N$) toric code model describing the dynamics of SU($N$) electric and magnetic fluxes on a two dimensional torus. We show that the model has $N^2$ topologically distinct ground states $\psi_0\rangle_{({\mathsf p},{\mathsf q})}$ which are loop states characterized by $Z_N \otimes Z_N$ centre charges $({\mathsf p},{\mathsf q} =0,1,2,\cdots, N1)$. We explicitly construct them in terms of coherent superpositions of all possible spin network states on torus with Wigner coefficients as their amplitudes. All excited quasiparticle states with SU($N$) electric charges and magnetic fluxes are constructed. We show that the braiding statistics of these SU(N) electric, magnetic quasiparticles or nonabelian anyons is encoded in the Wigner rotation matrices.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.13841
 Bibcode:
 2021arXiv211013841M
 Keywords:

 Quantum Physics;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 15 pages, 6 figures