2012/03/13 by Alejandro Cabo Montes de, Alejandro Cabo Montes de Oca, de Oca, Alejandro Cabo Montes
Chemistry · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Chemical and Physical Properties of Materials #FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el) #Superconductivity (cond-mat.supr-con) #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.1203.2689
17 pages, 8 figures
arxiv created 2012/03/13 · openalex publication_date 2012/03/13 · arxiv updated 2012/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A self-consistent formulation is proposed to generalize the HF scheme with the incorporation of screening effects. For this purpose in a first step, an energy functional is defined by the mean value for the full Hamiltonian, not in a Slater determinant state, but in the result of the adiabatic connection of Coulomb plus the nuclear (jellium charge) in the Slater determinant. Afterwards, the energy functional defining the screening approximation is defined in a diagrammatic way, by imposing a special "screening" restriction on the contractions retained in the Wick expansion. The generalized self-consisting set of equations for the one particle orbitals are written by imposing the extremum conditions. The scheme is applied to the homogeneous electron gas. After simplifying the discussion by assuming the screening as static and that the mean distance between electrons is close to the Bohr radius, the equations for the electron spectrum and the static screening properties are solved by iterations. The self-consistent results for the self-energies dispersion does not show the vanishing density of states at the Fermi level predicted by the HF self-energy spectrum. In this extreme non retarded approximation, both, the direct and the exchange potentials are strongly screened, and the energy is higher that the one given by the usual HF scheme. However, the inclusion of the retardation in the exact solution and the sum rules associated to the dielectric response of the problem, can lead to energy lowering. These effects will be considered in the extension of the work.