Symmetry protected invariants for the single-particle Green’s function of interacting topological insulators

The formalisms of topological quantum chemistry (TQC) [Bradlyn et al., Nature 547, 298 (2017)] and symmetry indicators [Po et al., Nature Communications 8, 50 (2017)] can be used to identify non-trivial topology protected by spatial symmetries in non-interacting lattice systems in all 230 space groups.
We extend these equivalent formalisms to interacting insulators in terms of the single-particle Matsubara Green's function in the zero-temperature limit. We do so by defining topological invariants for the Green's function at zero frequency which are protected by spatial symmetries. These invariants can be calculated by applying the formalism of TQC or symmetry indicators to an auxiliary non-interacting system defined by H_T(k) = -G^-1(0,k), which is known as the topological Hamiltonian [Wang et al., Phys. Rev. X 2, 031008 (2012)].
For general interacting systems these invariants can only change by (i) a gap closing in the spectral function at zero frequency, (ii) the Green's function having a zero at zero frequency or (iii) the Green's function breaking a protecting symmetry of the invariant.
We demonstrate the use of these invariants on the one-dimensional Su-Schrieffer-Heeger model with Hubbard interactions, which we solve by exact diagonalization for a finite number of unit cells.