  Topological phases originating from spin-orbit coupling have attracted great
attention recently. In this work, we use cellular dynamical mean field theory
with the continuous-time quantum Monte Carlo solver to study the
Kane-Mele-Hubbard model supplemented with an additional third-neighbor hopping
term. For weak interactions, the third-neighbor hopping term drives a
topological phase transition between a topological insulator and a trivial
insulator, consistent with previous fermion sign-free quantum Monte Carlo
results [H.-Hung et al., Phys. Rev. B 89, 235104 (2014)]. At finite
temperatures, the Dirac cones of the zero temperature topological phase
boundary give rise to a metallic regime of finite width in the third-neighbor
hopping. Furthermore, we extend the range of interactions into the strong
coupling regime and find an easy-plane anti-ferromagnetic insulating state
across a wide range of third-neighbor hopping. In contrast to the weak coupling
regime, no topological phase transition occurs at strong coupling, and the
ground state is a trivial anti-ferromagnetic insulating state. A comprehensive
finite temperature phase diagram in the interaction-third-neighbor hopping
plane is provided.
