Vison crystals in an extended Kitaev honeycomb model

We 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. The
extended model has a rich phase diagram containing five distinct vison crystals, as well as a
symmetric π-flux spin liquid with an approximate Fermi surface of Majorana fermions and a
sequence of topological Lifshitz transitions. We discuss possible experimental signatures and,
in particular, present finite-temperature Monte Carlo calculations of the specific heat and the
static vison structure factor. We argue that our extended model emerges naturally from generic
perturbations to the Kitaev honeycomb model.