Abstract
We construct an toric code model describing the dynamics of electric and magnetic fluxes on a two-dimensional torus. We show that the model has topologically distinct ground states , which are the loop states characterized by center charges . 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 electric charges and magnetic fluxes are constructed. We show that the braiding statistics of these electric or magnetic quasiparticles or non-Abelian anyons are encoded in the Wigner rotation matrices.
- Received 2 November 2021
- Accepted 10 January 2022
DOI:https://doi.org/10.1103/PhysRevA.105.052423
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