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

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.

Changes: Printing problems (due to non-standard macros) have been removed, 44 pages

Cited by in corpus (10)

• Time-dependent Gutzwiller approximation for the Hubbard model
• Z_2-slave-spin theory for strongly correlated fermions
• Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model
• Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model
• Critical properties of projected SO(5) models at finite temperatures
• Extended self-energy functional approach for strongly-correlated lattice bosons in the superfluid phase
• Magnetic Properties of the t-J Model in the Dynamical Mean-Field Theory
• Static overscreening and nonlinear response in the Hubbard Model
• On an exact criterion for choosing the hopping operator in the four-slave-boson approach
• Slave-boson based configuration-interaction approach for the Hubbard model