  We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading
each honeycomb plaquette. The resulting model has remarkably rich physical
properties. In each spin sector, the noninteracting band structure is
characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic
spin-orbit coupling $\lambda$ leads to a quadratic band crossing point
associated with a topological phase transition. At this point, quantum Monte
Carlo simulations reveal a magnetically ordered phase which extends to weak
coupling. Although the spinful model has two Kramers doublets at each edge and
is explicitly shown to be a $Z_{2}$ trivial insulator, the helical edge states
are protected at the single-particle level by translation symmetry. Drawing on
the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a
result of umklapp scattering for half-filled bands. For strong interactions,
this prediction is confirmed by quantum Monte Carlo simulations.
