Non-Abelian braid statistics as a holonomy in an exactly solvable lattice model

Jiannis Pachos

University of Leeds, School of Physics and Astronomy, UK

Kitaev's honeycomb lattice model is an exactly solvable model, where the vortices are conjectured to be non-Abelian Ising anyons. By employing the Majorana fermionization technique and exact diagonalization, we solve this model on a torus for arbitrary vortex configurations. This enables the evaluation of the non-Abelian holonomy associated with the adiabatic braiding of two vortices. We identify ranges in the parameters of the model where the holonomy coincides with the statistics of Ising anyons. Finally, we present an explicit scheme for the vortex creation, transport and characterization.

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