Year: 2022
Type: article
Abstract: We construct an $\mathrm{SU}(N)$ toric code model describing the dynamics of $\mathrm{SU}(N)$ electric and magnetic fluxes on a two-dimensional torus. We show that the model has ${N}^{2}$ topologically distinct ground states $|{\ensuremath{\psi}}_{0}{\ensuremath{\rangle}}_{(\mathsf{p},\mathsf{q})}$, which are the loop states characterized by ${Z}_{N}\ensuremath{\bigotimes}{Z}_{N}$ center charges $(\mathsf{p},\mathsf{q}=0,1,2,...,N\ensuremath{-}1)$. 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 $\mathrm{SU}(N)$ electric charges and magnetic fluxes are constructed. We show that the braiding statistics of these $\mathrm{SU}(N)$ electric or magnetic quasiparticles or non-Abelian anyons are encoded in the Wigner rotation matrices.
Source: Physical Review A
Authors: Manu Mathur, Atul Rathor
Institution: S.N. Bose National Centre for Basic Sciences
Language: Latvian
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3210063937