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Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model

We prove that the Kane-Mele-Hubbard model with purely imaginary next-nearest-neighbor hoppings has a particle-hole symmetry at half-filling. Such a symmetry has interesting consequences including the absence of charge and spin currents along open edges, and the absence of the sign problem in the determinant quantum Monte-Carlo simulations. Consequentially, the interplay between band topology and strong correlations can be studied at high numeric precisions. The process that the topological band insulator evolves into the antiferromagnetic Mott insulator as increasing interaction strength is studied by calculating both the bulk and edge electronic properties. In agreement with previous theory analyses, the numeric simulations show that the Kane-Mele-Hubbard model exhibits three phases as increasing correlation effects: the topological band insulating phase with stable helical edges, the bulk paramagnetic phase with unstable edges, and the bulk antiferromagnetic phase.