Three-dimensional topological phase on the diamond lattice

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice, which exhibits both Abelian and non-Abelian phases, the model has two ("weak" and "strong" pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a nonzero winding number introduced by Schnyder [Phys. Rev. B 78, 195125 (2008)] for the ensemble of Hamiltonians with both particle-hole and time-reversal symmetries. The topological character of the weak pairing phase is protected by a discrete symmetry.