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Journal of Physics Condensed Matter

On handling the measure in the slave-boson functional integral

Lew Gehlhoff, Raymond Frésard

Published Jan 8, 1996• 1 citation
Publisher

Abstract

We present an approach for dealing with the contribution following from the measure which occurs when going over from the Cartesian to the radial representation in the slave-boson functional integral. The connection with previous calculations is established and we treat as an example the one-band Hubbard model in the large-spin-degeneracy limit. The results that we obtain are in total agreement with those of a recent X-operator approach.

DOI
10.1088/0953-8984/8/2/001

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We present an approach for dealing with the contribution following from the measure which occurs when going over from the Cartesian to the radial representation in the slave-boson functional integral. The connection with previous calculations is established and we treat as an example the one-band Hubbard model in the large-spin-degeneracy limit. The results that we obtain are in total agreement with those of a recent X-operator approach.
Abstract We consider the large‐spin‐degeneracy (N) version of the U = ∞ one‐band Hubbard model and present a systematic 1/N expansion method which is based on Hubbard's X‐operator formulation and a Baym‐Kadanoff expansion. We compare this alternative X‐operator approach with the customary time‐continuum slave‐boson (SB) functional‐integral treatment, which has recently been criticized. In particular, we give a detailed derivation of the density Green's function within the new approach and compare the leading‐order results with those as obtained with the commonly used SB treatment, finding total agreement.
We study the single-band Hubbard model via the functional-integral four-slave-boson formulation introduced by Kotliar and Ruckenstein, and show that a proper treatment of the continuum limit of the functional integral removes the inconsistencies due to an incorrect handling of this limit so far performed in the literature. It follows from our analysis that the Kotliar and Ruckenstein mean-field solution has to be abandoned in order to include fluctuation corrections in a systematic way. We show explicitly how to construct a suitable alternative solution which admits the inclusion of fluctuations.
A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy DDD. 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=2D = 2D=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.
Abstract The functional integral formulation of the Hubbard model when treated in its Kotliar‐Ruckenstein representation in the radial gauge involves fermionic, as well as complex and radial slave boson fields. In order to improve on the understanding of the interplay of the three types of fields, and on the nature of the latter, a comprehensive investigation of an exactly solvable two‐site cluster is performed, as it entails all pitfalls embodied in this approach. It is first shown that the exact partition function is recovered, even when incorporating in the calculation the square root factors that are at the heart of the representation, when suitably regularized. It is shown that using radial slave boson fields allows to overcome all hurdles following from the normal ordering procedure. It is then demonstrated that this applies to the Green's function as well, and to the correlation functions of physical interest, thereby answering the criticisms raised by Schönhammer [K. Schönhammer, Phys. Rev. B 1990 42, 2591]. In addition, the investigation generalizes the calculations to the Hubbard model extended by a non‐local Coulomb interaction.
We study the Hubbard model through a functional-integral formulation proposed by Kotliar and Ruckenstein. A careful use of the U(1${)}^{\ensuremath{\bigotimes}3}$ gauge symmetry of the bosonized action allows us to compute the complete one-loop correction to the free energy in the case of half-filled band. We extract the effective mass of the fermion in the metallic phase and show that the noninteracting limit is not recovered for vanishing on-site repulsion. The bosonic Hamiltonian must be adjusted order by order in perturbation theory.