We show that the zero-temperature phase diagram of the vortex free sector of the Kitaev model is in one-to-one correspondence with that of the classical dimer model on the same lattice. We find that the model generically has three distinct phases. On a honeycomb lattice with a $3\times 3$ fundamental domain all three phases are accessible. As the couplings are varied, there are two distinct transitions. The new transition is one to a gapped phase that opens up in the interior of the $B$ phase.

• Received 15 December 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.147203