Kane-Mele-Hubbard model on theπ-flux honeycomb lattice

Abstract

We consider the Kane-Mele-Hubbard model with a magnetic $\ensuremath{\pi}$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\ifmmode\pm\else\textpm\fi{}2$. Fine-tuning of the intrinsic spin-orbit coupling $\ensuremath{\lambda}$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase that extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a ${Z}_{2}$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.