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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.
The emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident
We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective
Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability a
In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $N$ and plugged into the Dyson equation, which is then solved for the propagator $G_N$. For two simple
We present benchmark calculations of the Anderson lattice model based on the recently-developed ghost Gutzwiller approximation. Our analysis shows that, in some parameters regimes, the predictions of the standard Gutzwiller approximation can be incor