Γ-matrix generalization of the Kitaev model

Abstract

We extend the Kitaev model defined for the Pauli matrices to the Clifford algebra of $\ensuremath{\Gamma}$ matrices, taking the $4\ifmmode\times\else\texttimes\fi{}4$ 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 $\ensuremath{\Gamma}$ matrices are also discussed.