The Kane-Mele-Hubbard model in the Two-Particle Self-Consistent approach

The Kane-Mele model without interactions is well known to possess a quantized spin-Hall conductivity arising from topological effects of spin-orbit coupling (SOC). Adding a Hubbard interaction leads to a phase diagram that also features an anti-ferromagnetic phase. The interplay of anti-ferromagnetic spin fluctuations and topological properties can then be captured by our generalization of the Two-Particle Self-Consistent (TPSC) approach that includes the effect of spin-orbit coupling. TPSC is a many-body method, valid for weak to intermediate interaction strength that, with low computational effort, allows to investigate non-local correlation effects in interacting lattice models [1]. We present numerical results for the spin-Hall conductivity and discuss the role of anti-ferromagnetic spin fluctuations.

[1] Vilk, Tremblay J. Phys. I France, 7 11 (1997) 1309- 1368