  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.
