SU(N) toric code and non-Abelian anyons

Y We construct an 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 vertical bar psi(0)>((p,q)), which are the loop states characterized by Z(N) circle times Z(N) center charges (p, q = 0, 1, 2, ..., N - 1). We explicitly construct them in terms of coherent superpositions of all possible spin network states on a 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 or magnetic quasiparticles or non-Abelian anyons are encoded in the Wigner rotation matrices.

Automated summary

We construct a model describing the dynamics of SU(N) electric and magnetic fluxes and show the topological properties of its ground states. We also construct excited states of non-Abelian anyons and show their braiding statistics encoded in rotation matrices.