Gamma-matrix generalization of the Kitaev model

We extend the Kitaev model defined for the Pauli matrices to the Clifford algebra of Gamma matrices, taking the 4x4 representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically nontrivial phase carries gapless chiral edge modes along the sample boundary. On the three-dimensional (3D) diamond lattice, the ground states can exhibit gapless 3D Dirac-cone-like excitations and gapped topological insulating states. Generalizations to even higher rank Gamma matrices are also discussed.