  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.
