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arXiv · 1406.6077

Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice

Martin Bercx·Martin Hohenadler·Fakher F. Assaad
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Abstract

We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ 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 $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ 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 which 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.

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Martin Bercx, Martin Hohenadler, Fakher F. Assaad. 2014-06-23. Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice. https://doi.org/10.1103/physrevb.90.075140

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