Abstract
We investigate the interacting spinful Haldane model with on-site and nearest-neighbor repulsions on honeycomb lattices. Interactions drive spin-density and charge-density waves competing with each other. This competition enriches the phase diagram of the system greatly, where both topological and non-topological coexistence phases emerge with spin-density and charge-density wave orders. Moreover, the topological phase transition accompanied by the energy gap closure in coexistence phases is of third order. Finally, we study the topological properties consisting of Chern numbers and edge states for different phases.
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