No abstract

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro-and antiferromagnetism. Starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U , Bloch-bandwidth W , band occupation n, temperature T ) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second order phase transitions are found away from half filling, but close to half filling the system exhibits a tendency towards first order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (TC , TN ) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.

The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m 3 is conceptually important for a qualitatively correct description of the quasi-particle band structure in the strong-correlation regime. Different analytical approximations for the self-energy are analyzed with respect to their compatibility with the moment sum rule. To estimate the practical usefulness of the sum rule, correlation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different complexity are compared with each other and also with essentially exact results available for infinite-dimensional lattices. It turns out that the m 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic phase boundary as well as the critical temperature for the ferromagnetic phase on an f.c.c.-type lattice.

We propose a modified alloy analogy for the single-band Hubbard model, by which we investigate the possibility of spontaneous ferromagnetism in narrow energy bands. It is shown that a proper definition of the fictitious alloy enables self-consistent magnetic solutions to be found. The existence of spontaneous magnetism is mainly influenced by the lattice structure, the effective Coulomb coupling, and the band occupation. In accordance with the simple Stoner criterion, ferromagnetism appears in strongly correlated electron systems for band occupations, which locate the chemical potential in regions of high quasiparticle density of states. Rather realistic Curie temperatures are found. The macroscopic magnetic properties explain themselves via temperature-dependent quasiparticle densities of states, quasiparticle band structures, and respective spectral densities. It is shown how quasiparticle damping may depress quite substantially the stability of magnetic states by broadening corresponding spectral density peaks. Correlation effects lead to the expected splitting into two quasiparticle subbands ͑''Hubbard bands''͒, and under certain conditions to an additional exchange splitting of each of these quasiparticle subbands, as well as to a spin-dependent band narrowing, the combination of which gives rise to an unconventional ''inverse'' exchange shift at certain positions of the Brillouin zone.