Physics of Strong Correlations in Electronic Structure and Model Calculations

Sammanfattning: Using field theoretical methods models of strongly correlated electrons have been investigated. Application to electronic structure calculations has been made.In this thesis an attempt is made to build a bridge between first-principle band structure calculations and a theory of systems with strongly correlated electrons, by making use of perturbation theory from the atomic limit. Analyzing the total non-relativistic Hamiltonian leads to the basic model of strongly correlated systems, the Hubbard-Anderson model. In this thesis these basic models have been tested. Conclusions on delocalization and many-body aspects have been extracted from the solutions. Specifically for the lanthanides a separation of the f-system into two subsystems has resolved the discrepancy between calculated equilibrium volumes and experimental ones. The calculations are done within the Hubbard-I approximation, where it is possible to define renormalized fermion operators. The calculation is a true many-body calculation.Using perturbation theory a set of self consistent equations has been formulated, and solved, for praseodymium metal using the periodical Anderson model. The solution shows a self consistent decrease of the Hubbard U, and delocalization of the f-shell, when crucial parameters of the model are changed. The most salient feature of the models for strongly correlated electrons is the transfer of spectral weight from one energy region to another by adjusting pressure or other external parameters. The effects come from kinematic interactions that are important for strongly correlated systems.Investigations of the degenerate Hubbard model applied to the metal to insulator transition has also been made. When the degeneracy is considered, the transition to the metallic state occurs at smaller Coulomb energies. The validity of the Fermi liquid description for strongly correlated electrons has also been studied. The results show that the general behavior of the Fermi liquid state is quite robust.