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.
The novel slave-free (i.e. without slave bosons and fermions) approach to the problem of strong correlations is used in studying the Hubbard (t-J) model, where the self-energy is expressed in terms of charge and spin vertex functions of Hubbard operators. A systematic 1/N expansion (N is the number of spin components) of the self-energy is carried out. In O(1) it gives the same quasiparticle spectrum as the slave boson theory. The next order O(1/N) of the self-energy Σ(k, ω) is calculated exactly by solving analytically the integral equations for the charge and spin vertices. As an example for the feasibility of the proposed method explicit results for Σ(k, ω) are given in the case J=0. Dealing only with observable quantities our method is transparent and easily applicable to models which exclude double occupancy on lattice sites, such as the Anderson model and the Emery model for high temperature superconductors.
We examine the two existing slave-boson methods for the finite-U Hubbard model by Kotliar and Ruckenstein (KR) and by Newns et al. and Zou and Anderson (NZA) in the light of the Fermi-liquid quasiparticle picture. It is shown that to treat doubly occupied states the KR slave-boson scheme is more consistent with this picture and that the well-known erroneous gauge-symmetry breaking encountered in the mean-field treatment of the NZA double-occupancy boson is due to the presence of the hidden double-fermion operators. Then, the effective intersite antiferromagnetic interaction between quasiparticles is derived in the KR slave-boson approach by taking into account empty and double-occupancy slave-boson fluctuations to O(1/
N2) in the 1/N expansion of the functional-integral formalism. The obtained effective exchange coupling constant
Jeff(\ensuremath{\delta})=J(2
p02-\ensuremath{\delta}/2) with J\ensuremath{\equiv}
tij2/U is strongly dependent upon doping \ensuremath{\delta} and is scaled with the reduced Coulomb repulsion u\ensuremath{\equiv}U/
Uc in the two-dimensional (2D) and 3D Hubbard models, where
Uc is the critical value for the metal-to-insulator transition. The roles of this intersite correlation and the spin-dependent band-renormalization correlation included in the mean-field theory for the paramagnetic-to-antiferromagnetic instability are compared in the two Hubbard models. The intersite contribution is more significant in the 2D case than in the 3D case, but is generally small compared with the band effect except for small dopings \ensuremath{\delta} and smaller U values. The maximum doping ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$ for the paramagnetic-to-ferromagnetic instability in the strong-coupling limit (U\ensuremath{\rightarrow}\ensuremath{\infty}) of the 2D and 3D Hubbard models is found to be ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.28 and ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.38, respectively.
A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy
D. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate (
D=2) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.
We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model, where it systematically overestimates the importance of electronic correlation effects for weak interaction strength, by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.