A model to describe electronic correlations in energy bands is considered.
The model is a generalization of the conventional Hubbard model that allows for
the fact that the wavefunction for two electrons occupying the same Wannier
orbital is different from the product of single electron wavefunctions. We
diagonalize the Hamiltonian exactly on a four-site cluster and study its
properties as function of band filling. The quasiparticle weight is found to
decrease and the quasiparticle effective mass to increase as the electronic
band filling increases, and spectral weight in one- and two-particle spectral
functions is transfered from low to high frequencies as the band filling
increases. Quasiparticles at the Fermi energy are found to be more 'dressed'
when the Fermi level is in the upper half of the band (hole carriers) than when
it is in the lower half of the band (electron carriers). The effective
interaction between carriers is found to be strongly dependent on band filling
becoming less repulsive as the band filling increases, and attractive near the
top of the band in certain parameter ranges. The effective interaction is most
attractive when the single hole carriers are most heavily dressed, and in the
parameter regime where the effective interaction is attractive, hole carriers
are found to 'undress', hence become more like electrons, when they pair. It is
proposed that these are generic properties of electronic energy bands in solids
that reflect a fundamental electron-hole asymmetry of condensed matter. The
relation of these results to the understanding of superconductivity in solids
is discussed.Comment: Small changes following referee's comment
