Quantum spin Hall insulators with interactions and lattice anisotropy

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.