FUNCTIONAL-INTEGRAL FORMULATION OF THE SLAVE-BOSON APPROACH - BEYOND THE MEAN-FIELD TREATMENT WITH THE CORRECT CONTINUUM-LIMIT

We consider the widely adopted slave-boson method, which relies on a coherent-state functional-integral representation of the partition function and illustrate how to deal with the continuum imaginary time limit required by the very definition of the functional integral. We show that a correct treatment of the continuum limit of the functional integral modifies the free energy when fluctuation (1/N) corrections beyond the mean-field solution are considered. For the sake of definiteness, we consider a model Hamiltonian with an infinite (on-site) Hubbard repulsion. Numerical results are further presented for a two-level single-site model system. The additional terms in the free energy resulting from considering the correct continuum limit are shown to validate the 1/N expansion and to be consistent with relating the fluctuation results obtained via the ''radial'' and ''Cartesian'' gauges. Our analysis calls for a revision of several outcomes of the slave-boson method with the inclusion of fluctuation corrections.