Internal consistency of multi-tier GW+EDMFT

The multi-tier GW+EDMFT scheme is an ab-initio method for calculating the electronic structure of correlated materials. While the approach is free from ad-hoc parameters, it requires a selection of appropriate energy windows for describing low-energy and strongly correlated physics. In this study, we test the consistency of the multi-tier description by considering different low-energy windows for a series of cubic SrXO₃ (X = V, Cr, Mn) perovskites. Specifically, we compare the 3-orbital t_2g model, the 5-orbital t_2g + e_g model, the 12-orbital t_2g + O_p model, and (in the case of SrVO₃) the 14-orbital t_2g + e_g + O_p model and compare the results to available photoemission and X-ray absorption measurements. The multi-tier method yields consistent results for the t_2g and t_2g + e_g low-energy windows, while the models with O_p states produce stronger correlation effects and mostly agree well with experiment, especially in the unoccupied part of the spectrum. We also discuss the consistency between the fermionic and bosonic spectral functions and the physical origin of satellite features, and present momentum-resolved charge susceptibilities.