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Change of an insulator's topological properties by a Hubbard interaction

We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A topologically non-trivial insulator is then realized if there is one fermion per site. When interactions in the framework of the Hubbard model are introduced, the effective hopping parameters are renormalized and the system's topological number can change at a certain interaction strength, $U=\bar U$, smaller than that for the Mott transition. Two different situations may then occur: either the anomalous Hall conductivity $σ_{xy}$ changes abruptly at $\bar U$, as the system undergoes a transition from one topologically non-trivial insulator to another, or the transition is through an anomalous Hall metal, and $σ_{xy}$ changes smoothly between two different quantized values as $U$ grows. Restoring time-reversal symmetry by adding spin to spinless models, the half-filled system becomes a $\mathbb{Z}_2$ topological insulator. The topological number $ν$ then changes at a critical coupling $\bar U$ and the quantized spin Hall response changes abruptly.