  We study the interplay between spin-orbit coupling (SOC) and Coulomb
repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a
plethora of phases. While a quantum spin hall insulator is stable at weak
Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC
in a broad range of Coulomb repulsion. This semimetallic phase has topological
properties not observed in conventional metals such as a finite, non-quantized
spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit
coupling, electronic correlations stabilize a resonance valence bond (RVB) spin
liquid state in contrast to the classical antiferromagnetic state predicted by
mean-field theory. Under sufficiently strong SOC, such RVB state is transformed
into a magnetic insulator consisting on S~3/2 localized moments on a honeycomb
lattice with antiferromagnetic order and topological features.
