Anyons in an exactly solved model and beyond

Zhenghan Wang

Ijaz Durrani

Alberto G. Rojo, Geoffrey Canright

We present a multiplane model for the anyon problem. Anyons on different planes are coupled via a Coulomb–type interaction. We solve exactly finite clusters and show that the "antiferromagnetic" order of the chirality is favored for both attractive and repulsive interplane coupling. We also discuss a simple model that can be treated analytically and that has the same qualitative behavior as the exact results. Our results apply to the low density limit, in which finite currents exist in each plane. These currents also occur in the high temperature (nonsuperfluid) phase of the anyon system, and so our results should apply also to that regime.

Ville Lahtinen, Jiannis K. Pachos

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.

Diptiman Sen

Ijaz Durrani