Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry.

We study Gutzwiller-correlated wave functions as variational ground states for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a function of the impurity separation [Formula: see text]. Our variational state is obtained by applying the Gutzwiller many-particle correlator to a single-particle product state. We determine the optimal single-particle product state fully variationally from an effective non-interacting TIAM that contains a direct electron transfer between the impurities as variational degree of freedom. For a large Hubbard interaction U between the electrons on the impurities, the impurity spins experience a Heisenberg coupling proportional to [Formula: see text] where V parameterizes the strength of the on-site hybridization. For small Hubbard interactions we observe weakly coupled impurities. In general, for a three-dimensional simple cubic lattice we find discontinuous quantum phase transitions that separate weakly interacting impurities for small interactions from singlet pairs for large interactions.

Coulomb matrix elements in multi-orbital Hubbard models.

Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

Gutzwiller theory of band magnetism in LaOFeAs.

We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasiparticle bands of LaOFeAs. The Fe3d-As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parametrized by the Hubbard interaction U and an average Hund's-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 quasiparticles.

Gutzwiller variational theory for the Hubbard model with attractive interaction.

We investigate the electronic and superconducting properties of a negative-U Hubbard model. For this purpose we evaluate a recently introduced variational theory based on Gutzwiller-correlated BCS wavefunctions. We find significant differences between our approach and standard BCS theory, especially for the superconducting gap. For small values of |U|, we derive analytical expressions for the order parameter and the superconducting gap which we compare to exact results from perturbation theory.