Vison crystals in an extended Kitaev model on the Honeycomb latttice

I will introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and hence the integrability of the original model. This extended model emerges naturally from generic time reversal invariant perturbations to the Kitaev honeycomb model. The model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric -flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We will discuss possible experimental signatures of the different phases, including finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. Finally, we will see how different topologically ordered Z₂ quantum spin liquids with abelian and non-abelian anyons emerge naturally from this model, complementing the liquids with Chern numbers equal to 0, 1 and -1 that appear in the Kitaev honeycomb model.