Topological Green function of interacting systems

We construct a single-particle Green function, which can identify topological phases of interacting systems. The function is defined by an effective Bloch Hamiltonian, equal to the inverse full particles at zero frequency. Topological systems be detected coincidence poles and zeros diagonal components constructed function. crosses in momentum space are also signal nontrivial phases. As demonstration, we minimal model magnetic insulators. describes double exchange process between itinerant electrons moments presence spin-orbital coupling ionic potential electrons. identification zero's consistent with invariant. found antiferromagnetic state topologically breaking spin symmetry, where one orientation insulating state, while opposite trivial one.