Interacting Chern insulators: Diagrammatics well beyond the lowest order

We study phase diagram of the interacting spin-1/2 Haldane model with chiral phase φ=π/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. Conventional Quantum Monte Carlo methods, capable of dealing with "reasonable" system sizes, are ineffective here due to the fermionic sign problem. We employ the Diagrammatic Monte Carlo (DiagMC) technique to (i) accurately locate topologically nontrivial phases in the (△,U)-plane (△ is the inversion symmetry breaking on-site energy) and (ii) demonstrate the strong effect of typically discarded in theoretical considerations long-range part of the Coulomb interaction. The DiagMC technique is not subject to the conventional fermionic sign problem and allows one to deal with arbitrary shape of interaction potential in an approximations free manner. Final results with controlled accuracy are obtained by computing vertex corrections from higher-order diagrams until convergence is reached.