Non-Abelian statistics as a Berry phase in an exactly solvable model

We explicitly demonstrate the existence of non-Abelian anyons in Kitaev's honeycomb lattice model. This is achieved by employing exact eigenstates to simulate the adiabatic transport of the model's quasiparticles. The resulting Berry phase provides a direct demonstration of their non-Abelian statistics. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory.

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