A $\Gamma$-matrix generalization of the Kitaev model

TL;DR

This paper generalizes the Kitaev model using $ ext{Gamma}$-matrices, revealing new topological phases with chiral edge modes and Dirac cone excitations in 2D and 3D lattices.

Contribution

It introduces a $ ext{Gamma}$-matrix extension of the Kitaev model, exploring its topological phases and excitations on various lattice structures.

Findings

Ground state breaks time-reversal symmetry on decorated square lattice.

Presence of gapless chiral edge modes in the topological phase.

Gapless Dirac cone-like excitations in 3D diamond lattice.

Abstract

We extend the Kitaev model defined for the Pauli-matrices to the Clifford algebra of $\Gamma$-matrices, taking the $4 \times 4$ 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 non-trivial phase carries gapless chiral edge modes along the sample boundary. On the 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.