Ab initio study of the downfolded self-energy for correlated systems: Momentum dependence and effects of dynamical screening

The electronic structure of strongly correlated systems is usually calculated by using an effective model Hamiltonian with a small number of states and an effective on-site interaction. The mode, however, neglects the frequency dependence of the interaction, which emerges as a result of dynamical screening processes not included in the model. The self-energy calculated in this kind of model within dynamical mean-field theory (DMFT) is usually assumed to contain on-site components only. To study the validity of model calculations for the simulation of realistic materials, we make a detailed comparison between the downfolded self-energy in a model Hamiltonian with static and dynamic on-site interaction and the full ab initio self-energy for Fe and SrVO3 within the GW approximation. We find that the model GW self-energy shows weaker k (momentum) dependence than the ab initio GW self-energy, which is attributed to the lack of the long-range interaction and of contributions from other electrons not included in the models. This weak k dependence is found to lead to an artificial narrowing of the quasiparticle band structure. Moreover, this band narrowing is stronger for the dynamic (frequency-dependent) interaction, due to a larger renormalization of the quasiparticle states. These findings indicate a crucial role of the k dependence of the self-energy and dynamical screening for the electronic structure of correlated systems. We also discuss the effects beyond the GW approximation for correlated systems by comparing the GW and DMFT results.