  We study the phase diagram of the interacting spin-$1/2$ Haldane model with
chiral phase $\phi = \pi/2$ at half-filling. Both on-site and long-range
Coulomb repulsive interactions (Haldane-Hubbard-Coulomb model) are considered.
The problem with on-site interaction $U$ alone was addressed in the past by a
variety of approximate and finite size methods that produced results in
disagreement with each other both quantitatively and qualitatively. Here we
employ the Diagrammatic Monte Carlo technique to accurately locate phase
transition points to the topologically nontrivial phases in the $(\Delta,
U)$-plane, where $\pm \Delta$ is the inversion symmetry breaking on-site
energy, and establish that momentum dependence of self-energy cannot be
neglected in the proper treatment. We also find that even modest long-range
interactions, typically discarded in theoretical considerations, result in
significant shifts of transition lines.
