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The Z2 topological invariant, spin Chern number and zero-frequency Green's functions in correlated topological insulators

The stability of topological insulators under electronic correlation has been an elusive yet central topic. In this talk, we will discuss the correlation effects in the two descendants of the Kane-Mele-Hubbard model, called generalized Kane-Mele-Hubbard model and dimerized Kane-Mele-Hubbard model, by means of the sign-free Quantum Monte Carlo (QMC) method. In the non-interacting limit, both systems undergo topological phase transitions by tuning tight-binding (one-body) parameters. Under interaction, we can compute the topological invariant, the Z2 invariant and spin Chern number, and observe the zero-frequency Green's function behavior to identify the phase transition in finite-size clusters with the QMC. We found that the quantum fluctuations from interaction may either stabilize or destabilize the topological insulator phase in the KMH models, depending on the symmetry character of the one-body parameter. Our numerical results suggest that if the one-body term preserves the lattice symmetry, correlation stabilizes the topological insulators whereas in other cases it usually destabilizes.

(1) Hsiang-Hsuan Hung, Lei Wang, Zheng-Cheng Gu, Gregory A. Fiete, Phys. Rev. B  87, 121113(R) (2013)
(2) Hsiang-Hsuan Hung, Victor Chua, Lei Wang, Gregory A. Fiete, arXov: 1307.2659
(3) Zi Yang Meng, Hsiang-Hsuan Hung, Thomas C. Lang, arXiv: 1310.6064