Within the binary, self-consistent static approximation to the Hubbard-model, local moments are created out of itinerant electrons. The magnetic Ising-type interactions of these local moments are calculated and explicit results are obtained. Relaxing the static character of the approximation transforms the interactions to Heisenberg type and renormalises their size. Renormalisation is necessary in order to satisfy certain sum rules. The authors' results are in good agreement with exact many-body results.
Within the binary, self-consistent static approximation to the Hubbard-model, local moments are created out of itinerant electrons. The magnetic Ising-type interactions of these local moments are calculated and explicit results are obtained. Relaxing the static character of the approximation transforms the interactions to Heisenberg type and renormalises their size. Renormalisation is necessary in order to satisfy certain sum rules. The authors' results are in good agreement with exact many-body results.
The static approximation in the functional integral theory of itinerant magnetism is critically investigated. For the two-site Hubbard model the local magnetic moment and the specific heat are calculated as functions of temperature and interaction strength. By comparison with the exact results the error in the static approximation is found to be large at low temperatures and for small interaction strengths. It is shown that the subdivision of the ground state into a phase without a local moment (small interaction) and a phase with local moment (large interaction) is induced by the static approximation. The specific heat is underestimated and the zero-point entropy is finite. The implications for the infinite Hubbard model are briefly discussed.
We derive the random-phase approximation for spin excitations in general multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock ground state. The results are compared with those from a recently introduced variational many-body approach to spin waves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the Hartree-Fock theory fails to describe properly the local moments which naturally arise in a correlated-electron theory.
Using the Dyson equation of motion for both the diagonal one-particle Green function, G(k,ω) and off--diagonal Green function, F(k,ω), at the level of the Hubbard--I decoupling scheme, we have found that they have four poles symmetric in pairs, justifying a more elaborated calculation done by the Zürich group by means of the T-Matrix approach (Pedersen et al, Z. Physik B {\bf 103}, 21 (1997)) and the moment approach of Nolting (Z. Physik {\bf 255}, 25 (1972)). We find that the energy spectra and the weights of G(k,ω) and F(k,ω) have to be calculated self-consistently. G(k,ω) satisfies the first two moments while F(k,ω) the first sum rule. Our {\it order parameter} α(T) is given by 1/Ns∑kε(k)Δ(k). Due to the fact that we have a purely local attractive interaction Δ(k) can be of {\it any} s--type wave. However, for a {\it pure s--wave}, for which α(T)=0, we go back to the mean--field BCS results, with a renormalized chemical potential. In this case, the off--diagonal Green function, F(k,ω), satisfies the first two off--diagonal sum rules. We explicitly state the range of validity of our approximation.
After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.
The authors construct a diagram technique for the (t-J) model Hamiltonian expressed in terms of Hubbard operators. This technique combines features of the diagram technique for normal Fermi systems and those for the Heisenberg model with spin operators. The general graphic structure is identified for one-particle Green functions composed of Hubbard operators. The (t-J) model has logical consistency, is reasonably simple and can serve as a working tool in exploring various properties of this model. To an approximation that resides in summing ladder-type diagrams with antiparallel electron lines, the authors calculate the system's magnetic susceptibility. A formula is derived which reflects the dual nature of the magnetic states in the Hubbard model; this duality manifests itself in the presence of a localised and an itinerant contribution in the bare susceptibility. The authors trace how the relative value of the localised contribution varies as the electron concentration is increased from 0 to 1. With n>2/3, the paramagnetic phase of the system becomes unstable with respect to the occurrence of ferromagnetic or antiferromagnetic ordering. A magnetic phase diagram for zero temperature is constructed on the (t/U, n) plane.
The interaction energy $W[\ensuremath{\gamma}]$ of the Hubbard model is regarded as a functional of the single-particle density matrix $\ensuremath{\gamma}$ in the framework of lattice density-functional theory. The local character of the Hubbard interaction is exploited to express W as a sum of local contributions ${\ensuremath{\omega}}_{i}[\ensuremath{\gamma}]$, for which a simple semilocal scaling approximation is proposed. The method is applied to the ionic Hubbard model on one- and two-dimensional lattices with homogeneous and inhomogeneous Coulomb repulsions. Results are given for the kinetic and Coulomb energies, interatomic charge transfers, local magnetic moments, and charge gaps. Goals and limitations of the functional are discussed by comparison with exact results.