  We investigate the interplay between spin-orbit coupling and
electron-electron interactions on the honeycomb lattice combining the cellular
dynamical mean-field theory and its real space extension with analytical
approaches. We provide a thorough analysis of the phase diagram and temperature
effects at weak spin-orbit coupling. We systematically discuss the stability of
the quantum spin Hall phase toward interactions and lattice anisotropy
resulting in the plaquette-honeycomb model. We also show the evolution of the
helical edge states characteristic of quantum spin Hall insulators as a
function of Hubbard interaction and anisotropy. At very weak spin-orbit
coupling and intermediate electron-electron interactions, we substantiate the
existence of a quantum spin liquid phase.
