Including many-body screening into self-consistent calculations--tight-binding model studies with Gutzwiller approximation*

We introduce a scheme to include many-body screening process explicitly into self-consistent equations for electronic structure calculations by employing Gutzwiller approximation. The method is illustrated by applying to a tight-binding model of the strongly correlated $\gamma$-Ce. The critical Coulomb repulsion $U_{ff}^{c}$ between the $4f$ electrons for electronic phase transition can be greatly raised over the usual screened value by including the main onsite many-body screening $5d$ channels. The method provides a promising way towards parameter-free \textit{ab initio} Gutzwiller density functional theory.