Topological invariants in interacting Quantum Spin Hall: a Cluster   Perturbation Theory approach
  Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided. 
F. Grandi, F. Manghi, O. Corradini, C.M. Bertoni and A. Bonini
cond-mat.str-el