Topological invariants in interacting quantum spin Hall: a cluster perturbation theory approach

Using cluster perturbation theory we calculate Greenʼs functions, quasi-particle energies and topological invariants for interacting electrons on a 2Dhoneycomb lattice, with intrinsic spin–orbit coupling and on-site e–e interaction. This allows us to define the parameter range (HubbardUversus 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.Wehave 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.