CORRECT CONTINUUM-LIMIT OF THE FUNCTIONAL-INTEGRAL REPRESENTATION FORTHE 4-SLAVE-BOSON APPROACH TO THE HUBBARD-MODEL - PARAMAGNETIC PHASE

The Hubbard model with finite on-site repulsion U is studied via the f unctional-integral formulation of the four-slave-boson approach by Kot liar and Ruckenstein. It is shown that a correct treatment of the cont inuum imaginary time limit (which is required by the very definition o f the functional integral) modifies the free energy when fluctuation ( 1/N) corrections beyond mean field are considered, thus removing the i nconsistencies originating from the incorrect handling of this patholo gic limit so far performed in the literature. In particular, our treat ment correctly restores the decrease of the average number of doubly o ccupied sites for increasing U. Our analysis requires us to suitably i nterpret the Kotliar and Ruckenstein choice for the bosonic hopping op erator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative c hoices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily availa ble for any U. We also discuss how the 1/N expansion can be formally g eneralized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which r esult at the order 1/N from the correct continuum limit.