We give a comprehensive introduction into an efficient numerical scheme for the minimisation of Gutzwiller energy functionals in studies on multi-band Hubbard models. Our method covers all conceivable cases of Gutzwiller variational wave functions an
d has been used successfully in previous numerical studies.
We study the correlation-induced deformation of Fermi surfaces by means of a new diagrammatic method which allows for the analytical evaluation of Gutzwiller wave functions in finite dimensions. In agreement with renormalization-group results we find
Pomeranchuk instabilities in two-dimensional Hubbard models for sufficiently large Coulomb interactions.
We use the Gutzwiller variational theory to investigate the electronic and the magnetic properties of fcc-Nickel. Our particular focus is on the effects of the spin-orbit coupling. Unlike standard relativistic band-structure theories, we reproduce th
e experimental magnetic moment direction and we explain the change of the Fermi-surface topology that occurs when the magnetic moment direction is rotated by an external magnetic field. The Fermi surface in our calculation deviates from early de-Haas--van-Alphen (dHvA) results. We attribute these discrepancies to an incorrect interpretation of the raw dHvA data.
