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Abstract
In this Rapid Communication we study the Haldane model with on-site repulsive interactions at half-filling. We show that the mean-field Hamiltonian with magnetic order effectively modifies parameters in the Haldane Hamiltonian, such as sublattice energy difference and phase in next-nearest hopping. As interaction increases, increasing of magnetic order corresponds to varying these parameters and, consequently, drives topological transitions. At the mean-field level, one scenario is that the magnetic order continuously increases, and, inevitably, the fermion gap closes at the topological transition point. Beyond the mean field, fluctuation-induced interaction can further open up the gap, rendering a first-order transition. Another scenario is a first-order transition at the mean-field level across which a canted magnetic order develops discontinuously, avoiding the fermion gap closing. We find that both scenarios exist in the phase diagram of the Haldane-Hubbard model. Our predication is relevant to recent experimental realization of the Haldane model in cold-atom system.
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