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 $|{\psi }_0{⟩}_{(\mathsf{p},\mathsf{q})}$ which are loop states characterized by $Z_N\otimes Z_N$ centre charges $(\mathsf{p},\mathsf{q}=0,1,2,\cdots ,N-1)$. 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.

arXiv comment15 pages, 6 figures,published in Physical Review A

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Cited by in corpus (1)

• Stabilizer Codes with Exotic Local-dimensions