The effect of electron correlations in the infinite-dimension (d=∞) Hubbard model at finite temperatures has been investigated with the use of a theory which was recently proposed by the present author generalizing the slave-boson functional-integral method. Sublattice magnetizations, double occupancies and band-narrowing factors are computed as functions of the interaction, U, and the temperature, T. Calculated results are exact in the limits of U→0 and U→∞, and in the limits of T=0 and T→∞ they are expected to be very accurate owing to the nature of our mean-field-type theory for infinite-dimension systems. Similarities and differences between the calculated results for d=3 and d=∞ are also discussed.
Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral
t equals the correlated hopping integral
X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of
X and any electron concentration
n. At the half-filled band
(n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for
n close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral
U close to the phase-transition point.
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 wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a 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 transferred 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.
We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model, formulated in terms of thermal Green's functions, shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.
Using the slave-boson method in its spin-and charge-rotational invariant representation we determine stability of the superconducting state in the Hubbard model with correlated hopping.In general the term with correlated hopping violates electron-hole symmetry, however, in the special case when the correlated hopping integral X is equal to the uncorrelated hopping inte- gral t the electron-hole symmetry remains.We investigate this case and show that correlations induced by onsite Coulomb interactions U yield to the nor- mal state with exactly single occupied sites (corresponding to |U = oo)).The phase diagram of the superconducting state is determined for the different electron concentration n.At the half-filled band (n = 1) a direct transition from the Mott insulator to the superconducting state occurs.