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

Degenerate Hubbard models are studied using the Generalized-Gutzwiller-Approximation. It is found that the metal-insulator transition occurs at a finite correlation $U_c$ when the average number of electrons per lattice site is an integer. The critical $U_c$ depends sensitively on both the band degeneracy $N$ and the filling $x$. A derivation is presented for the general expression of $U_c(x,N)$ which reproduces all previously known Gutzwiller solutions, including that of the...

Multi-band Gutzwiller-correlated wave functions reconcile the contrasting concepts of itinerant band electrons versus electrons localized in partially filled atomic shells. The approximate evaluation of these variational ground states becomes exact in the limit of large coordination number. The result allows the identification of quasi-particle band structures for correlated electron systems. As a first application, we summarize a study of itinerant ferromagnetism in a two-ba...

A novel effective Hamiltonian in the subspace of singly occupied states is obtained by applying the Gutzwiller projection approach to a generalized Hubbard model with the interactions between two nearest- neighbor sites. This model provides a more complete description of the physics of strongly correlated electron systems. The system is not necessarily in a ferromagnetic state as temperature approaches zero at any doping level. The system, however, must be in an antiferromagn...

An orbitally degenerate two-band Hubbard model is analyzed with inclusion of the Hund's rule induced spin-triplet 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 Hund's rule coupling strength and the band filling. Also, the influence of the inters...

We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $\psi=\exp(-\lambda K)P_G\psi_0$, where $\psi_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $\lambda$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity...

We formulate a multi-band generalisation of the time-dependent Gutzwiller theory. This approach allows for the calculation of general two-particle response functions, which are crucial for an understanding of various experiments in solid-state physics. As a first application, we study the momentum- and frequency-resolved magnetic susceptibility in a two-band Hubbard model. Like in the underlying ground-state approaches we find significant differences between the results of ou...

Ground-state properties, such as energies and double occupancies, of a one-dimensional two-band Hubbard model are calculated using a first principles Gutzwiller conjugate gradient minimization theory. The favorable agreement with the results from the density matrix renormalization group theory demonstrates the accuracy of our method. A rotationally invariant approach is further incorporated into the method to greatly reduce the computational complexity with a speedup of 300 t...

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 properties (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 st...

The minimum of the Gutzwiller energy functional depends on the number of parameters considered in the variational state. For a three-orbital Hubbard model we find that the frequently used diagonal Ansatz is very accurate in high-symmetry situations. For lower symmetry, induced by a crystal-field splitting or the spin-orbit coupling, the discrepancies in energy between the most general and a diagonal Gutzwiller Ansatz can be quite significant. We discuss approximate schemes th...

The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction $U$ increases. The antiferromagnetic correlation induced by...