Topological phase transitions driven by gauge fields in an exactly solvable model

We demonstrate the existence of a topologically ordered phase in Kitaev's honeycomb lattice model. This phase appears due to the presence of a vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its low-energy behavior that is described by a distinct number of Dirac fermions. We identify two physically distinct types of topological phase transitions and obtain analytically the critical behavior of the extended phase space. The Fermi-surface evolution associated with the transitions is shown to be due to the Dirac fermions coupling to chiral gauge fields. Finally, we describe how the phase can be understood in terms of interactions between the anyonic vortices.