Topological invariants for interacting topological insulators with inversion symmetry

For interacting Z₂ topological insulators with inversion symmetry, we propose a simple topological invariant expressed in terms of the parity eigenvalues of the interacting Green's function at time-reversal invariant momenta and zero frequency. We derive this result from our previous formula involving the integral over the frequency-momenta space. This formula greatly simplifies the explicit calculation of Z₂ topological invariants in inversion-symmetric insulators with strong interactions.