Including many-body screening into self-consistent calculations: Tight-binding model studies with the Gutzwiller approximation

We introduce a scheme to include many-body screening processes explicitly into a set of self-consistent equations for electronic structure calculations using the Gutzwiller approximation. The method is illustrated by the application to a tight-binding model describing the strongly correlated {\gamma}-Ce system. With the inclusion of the 5d-electrons into the local Gutzwiller projection subspace, the correct input Coulomb repulsion U_{ff} between the 4f-electrons for {\gamma}-Ce in the calculations can be pushed far beyond the usual screened value U_{ff}^{scr} and close to the bare atomic value U_{ff}^{bare}. This indicates that the d-f many-body screening is the dominant contribution to the screening of U_{ff} in this system. The method provides a promising way towards the ab initio Gutzwiller density functional theory.