On the correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

TL;DR

This paper refines the four-slave-boson approach to the Hubbard model by correctly handling the continuum limit in the functional integral, improving fluctuation correction accuracy and matching exact solutions at U=0.

Contribution

It introduces a proper treatment of the continuum imaginary time limit and reinterpretation of bosonic operators, enhancing the four-slave-boson method's accuracy beyond mean-field.

Findings

Correctly accounts for fluctuation corrections beyond mean-field

Recovers exact U=0 solution at next order in 1/N

Provides a numerical test of alternative bosonic hopping operators

Abstract

The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean-field are considered. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator 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 choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.