Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator

We provide a self-consistent mean-field framework to study the effect of strong interactions in a quantum spin Hall insulator on the honeycomb lattice. We identify an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction. This phase is gapped in the bulk, has gapless edge states and does not break any symmetry. Instead, we find a four-fold topological degeneracy of the ground state on the torus and fractionalized excitations with semionic mutual braiding statistics. Our work highlights the important theme that interesting phases arise in the regime of strong spin-orbit coupling and interactions.