The Generalized Gutzwiller Method for n=>2 Correlated Orbitals: Itinerant Ferromagnetism in eg-bands

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 evaluation 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 expans...

We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of infinite spatial dimensions. In this limit recent results obtained within the Gutzwiller approximation are seen to become exact for these wave functions. We further show that the Slave Boson mean-field theory for degenerate bands becomes vari...

We introduce a new type of Gutzwiller variational wavefunction for correlated electrons coupled to phonons, able to treat on equal footing electronic and lattice degrees of freedom. We benchmark the wavefunction in the infinite-$U$ Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can directly compare with exact results by Dynamical Mean-Field Theory. For this model, we find that variational results agree perfectly well with the exact ones. In particu...

To understand effects of orbital degeneracy on magnetism, in particular effects of Hund's rule coupling, we study the two-orbital Hubbard model on a square lattice by a variational Monte Carlo method. As a variational wave function, we consider a Gutzwiller projected wave function for a staggered spin and/or orbital ordered state. We find a ferromagnetic phase with staggered orbital order around quarter-filling, i.e., electron number n=1 per site, and an antiferromagnetic pha...

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. {\bf 86}, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the do...

The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the motivation for its development to the formulation of the Hamiltonian,and some methods of calculation within the model. The second part will discuss some applications of the model to 1D and 2D systems,based on a combination of the author's results wi...

We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various...

We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. The formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement ove...

In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated Gutzwiller Wave Function (GWF). We discuss the available methods for evaluating $W$, in particular the recently proposed diagrammatic expansion method. We compare the two existing approaches to minimize $W$: the standard approach based on th...

Ferromagnetic Nickel is the most celebrated iron group metal with pronounced discrepancies between the experimental electronic properties and predictions of density functional theories. In this work, we show in detail that the recently developed multi-band Gutzwiller theory provides a very good description of the quasi-particle band structure of nickel. We obtain the correct exchange splittings and we reproduce the experimental Fermi-surface topology. The correct (111)-direct...