We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evalu
ation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.
We present a detailed derivation of the Gutzwiller Density Functional Theory that covers all conceivable cases of symmetries and Gutzwiller wave functions. The method is used in a study of ferromagnetic nickel where we calculate ground state properti
es (lattice constant, bulk modulus, spin magnetic moment) and the quasi-particle band structure. Our method resolves most shortcomings of an ordinary Density Functional calculation on nickel. However, the quality of the results strongly depends on the particular choice of the double-counting correction. This constitutes a serious problem for all methods that attempt to merge Density Functional Theory with correlated-electron approaches based on Hubbard-type local interactions.
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 use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasi-particle bands of LaOFeAs. The Fe3d--As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard mod
el. The full atomic interaction between the electrons in the iron orbitals is parameterized by the Hubbard interaction U and an average Hunds-rule interaction J. We reproduce the experimentally observed small ordered magnetic moment over a large region of (U,J) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasi-particles.
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 investigate multi-band Hubbard models for the three iron 3$d$-$t_{2g}$ bands and the two iron 3$d$-$e_g$ bands in ${rm La O Fe As}$ by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Har
tree--Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree--Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hunds-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron $e_g$ electrons polarize the $t_{2g}$ electrons and they substantially contribute to the ordered moment.
