  We construct a Green function, which can identify the topological nature of
interacting systems. It is equivalent to the single-particle Green function of
effective non-interacting particles, the Bloch Hamiltonian of which is given by
the inverse of the full Green function of the original interacting particles at
zero frequency. The topological nature of the interacting insulators is
originated from the coincidence of the poles and the zeros of the diagonal
elements of the constructed Green function. The cross of the zeros in the
momentum space closely relates to the topological nature of insulators. As a
demonstration, using the zero's cross, we identify the topological phases of
magnetic insulators, where both the ionic potential and the spin exchange
between conduction electrons and magnetic moments are present together with the
spin-orbital coupling. The topological phase identification is consistent with
the topological invariant of the magnetic insulators. We also found an
antiferromagnetic state with topologically breaking of the spin symmetry, where
electrons with one spin orientation are in topological insulating state, while
electrons with the opposite spin orientation are in topologically trivial one.
