Jörg Bünemann

MULTIBAND GUTZWILLER WAVE FUNCTIONS FOR GENERAL ON-SITE INTERACTIONS

We introduce Gutzwiller wave functions for multi-band models with general on-site Coulomb interactions. As these wave functions employ correlators for the exact atomic eigenstates they are exact both in the non-interacting and in the atomic limit. We evaluate them in infinite lattice dimensions for all interaction strengths without any restrictions on the structure of the Hamiltonian or the symmetry of the ground state. The results for the ground-state energy allow us to derive an effective one-electron Hamiltonian for Landau quasi-particles, applicable for finite temperatures and frequencies within the Fermi-liquid regime. As applications for a two-band model we study the Brinkman-Rice metal-to-insulator transition at half band-filling, and the transition to itinerant ferromagnetism for two specific fillings, at and close to a peak in the density of states of the non-interacting system. Our new results significantly differ from those for earlier Gutzwiller wave functions where only density-type interactions were included. When the correct spin symmetries for the two-electron states are taken into account, the importance of the Hunds-rule exchange interaction is even more pronounced and leads to paramagnetic metallic ground states with large local magnetic moments. Ferromagnetism requires fairly large interaction strengths, and the resulting ferromagnetic state is a strongly correlated metal.

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 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 quasiparticles.

Atomic correlations in itinerant ferromagnets: Quasi-particle bands of nickel

The Gutzwiller theory is demonstrated to resolve most of the long-standing discrepancies between experiment and theory on the quasi-particle bands of ferromagnetic nickel. This is confirmed by new angle-resolved photoelectron spectroscopy data along various high-symmetry lines of the bulk Brillouin zone obtained under full control of the three-dimensional momentum. Our findings support the view of itinerant ferromagnetism as a consequence of atomic correlations.

Even-parity spin-triplet pairing by purely repulsive interactions for orbitally degenerate correlated fermions

We demonstrate the stability of a spin-triplet paired s-wave (with an admixture of extended swave) state for the case of purely repulsive interactions in a degenerate two-band Hubbard model. We further show that near half-filling the considered kind of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation for the case of a square lattice. The absence of a stable paired state when analyzed in the Hartree-Fock-BCS approximation allows us to claim that the electron correlations in conjunction with the Hund’s rule exchange play the crucial role in stabilizing the spin-triplet superconducting state. A sizable hybridization of the bands suppresses the paired state.We demonstrate the stability of the spin-triplet paired s-wave (with an admixture of extended s-wave) state for the limit of purely repulsive interactions in a degenerate two-band Hubbard model of correlated fermions. The repulsive interactions limit represents an essential extension of our previous analysis (2013 New J. Phys. 15 073050), regarded here as I. We also show that near the half-filling the considered type of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation (SGA) for the case of a square lattice. We suggest that the electron correlations in conjunction with the Hunds rule exchange play the crucial role in stabilizing the real-space spin-triplet superconducting state. A sizable hybridization of the bands suppresses the homogeneous paired state.

Coexistence of spin-triplet superconductivity with magnetism within a single mechanism for orbitally degenerate correlated electrons: statistically consistent Gutzwiller approximation

An orbitally degenerate two-band Hubbard model is analyzed with the inclusion of the Hunds rule-induced spin-triplet even-parity paired states and their coexistence with magnetic ordering. The so-called statistically consistent Gutzwiller approximation (SGA) has been applied to the case of a square lattice. The superconducting gaps, the magnetic moment and the free energy are analyzed as a function of the Hunds rule coupling strength and the band filling. Also, the influence of the intersite hybridization on the stability of paired phases is discussed. In order to examine the effect of correlations the results are compared with those calculated earlier within the Hartree-Fock (HF) approximation combined with the Bardeen-Cooper-Schrieffer (BCS) approach. Significant differences between the two methods used (HF+BCS versus SGA+real-space pairing) appear in the stability regions of the considered phases. Our results supplement the analysis of this canonical model used

Variational study of Fermi surface deformations in Hubbard models

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.

High-temperature superconductivity in the two-dimensional t-J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t–J model with the hopping electron amplitudes t (and ) between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the methodʼs results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed ‘grand-canonical Gutzwiller approximation’ (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the k-space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly correlated systems, as it (i) works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to that of the GA (i.e., it provides the results much faster than the VMC approach).

Renormalization of bulk magnetic electron states at high binding energies.

The quasiparticle dynamics of electrons in a magnetically ordered state is investigated by high-resolution angle-resolved photoemission of Ni(110) at 10 K. The self-energy is extracted for high binding energies reaching up to 500 meV, using a Gutzwiller calculation as a reference frame for correlated quasiparticles. Significant deviations exist in the 300 meV range, as identified on magnetic bulk bands for the first time. The discrepancy is strikingly well described by a self-energy model assuming interactions with spin excitations. Implications relating to different electron-electron correlation regimes are discussed.

Spin-orbit coupling in ferromagnetic nickel.

We use the Gutzwiller variational theory to investigate the electronic and 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 the 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 results. We attribute these discrepancies to an incorrect interpretation of the raw de Haas-van Alphen data.

Landau-Gutzwiller quasiparticles

We define Landau quasiparticles within the Gutzwiller variational theory and derive their dispersion relation for general multiband Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were based on a phenomenological effective single-particle Hamiltonian. For the one-band Hubbard model we calculate the frst-order corrections in 1/D and find that the corrections to the quasiparticle dispersions are small in three dimensions. They may be largely absorbed in a rescaling of the total bandwidth, unless the system is close to half band filling. Therefore, the Gutzwiller theory in the limit of large dimensions provides quasiparticle bands which are suitable for a comparison with real, three-dimensional Fermi liquids.