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.
We investigate the possibility of superconductivity in the large-
U limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended
s-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.
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.
The application of functional integral methods and the Hubbard--Stratonovich transformation to the Hubbard model is discussed. For the attractive case, using a simple gauge transformation of the superconducting order parameter field, the effective action for the low-energy phase excitations is derived. Inclusion of the electromagnetic field is straightforward. For the repulsive case at half--filling use of a fluctuating spin reference frame allows a derivation of the effective nonlinear sigma model for arbitrary coupling strength U. Results for the spin-wave velocity and the spin stiffness are obtained for arbitrary U. Away from half--filling, at large U an effective action for doped fermions and the spins is found which is related to the slave fermion formulation of the correlated fermion problem. The formalism is generalized to include the full SU(2)xSU(2) symmetry of the Hubbard model. This allows the derivation of a Ginzburg-Landau like theory that includes both particle-hole and particle-particle excitations. (paper at the NATO workshop on the Hubbard model, San Sebastian, Spain, oct. 1993)
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.