A variational approach for calculating Auger electron spectra: going beyond the impurity approximation

We propose a novel variational method to calculate the two-hole propagators relevant for Auger spectroscopy in transition metal oxides. This method can be thought of as an intermediary step between the full solution (which is difficult to generalize to systems with partially filled bands) and the impurity approximation. Like the former, our solution has full translational invariance, and like the latter, it can be generalized to certain types of systems with partially filled bands. Here we compare both our variational approximation and the impurity approximation against the exact solution for a simple one-dimensional model with filled bands. We show that when the energies of the eigenstates residing primarily on the transition metal ions do not overlap with those of the eigenstates residing primarily on Oxygen ions, both approximations are valid but the variational approach is superior.