Poisson equation and self-consistent periodical Anderson model

We show that the formally exact expression for the free energy (with a non-relativistic Hamiltonian) for the correlated metal generates the Poisson equation within the saddle-point approximation for the electric potential, where the charge density automatically includes correlations. In this approximation the problem is reduced to the self-consistent periodical Anderson model (SCPAM). The parameter of the mixing interaction in this formulation have to be found self-consistently together with the correlated charge density. The factors, calculated by Irkhin, for the mixing interaction, which reflect the structure of the many-electron states of the \f-ion involved, arise automatically in this formulation and are quite sensitive to the specific element we are interested in. We also discuss the definitions of the mixing interaction for the mapping from ab initio to model calculations.Comment: 25 pages, no figure

Theory of strongly correlated f and d-electron systems. I. Exact Hamiltonian, Hubbard-Anderson models and perturbation theory near atomic limit within non-orthogonal basis set

The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym-Kadanoff method for correlated systems.Comment: 40 pages, 6 figure

Modification of the standard model for the lanthanides

We show that incorporation of strong electron correlations into the Kohn-Sham scheme of band structure calculations leads to a modification of the standard model of the lanthanides and that this procedure removes the existing discrepancy between theory and experiment concerning the ground state properties. Within the picture suggested, part of the upper Hubbard $f$-band is occupied due to conduction band-$f$-mixing interaction (that is renormalized due to correlations) and this contributes to the cohesive energy of the crystal. The lower Hubbard band has zero width and describes fermionic excitations in the shell of localized $f$-s. Fully self-consistent calculations (with respect to both charge density and many-electron population numbers of the $f$-shell) of the equilibrium volume $V_0$ and the bulk modulus of selected lanthanides have been performed and a good agreement is obtained.Comment: 1 fi