Γ-matrix generalization of the Kitaev model

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