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Physics Reports

Functional-integral formulation of the slave-boson approach: Beyond the mean-field treatment with the correct continuum limit

Enrico Arrigoni, Claudio Castellani, M. Grilli, Roberto Raimondi, Giancarlo Calvanese Strinati

Published Jun 1, 1994• 30 citations
Publisher
DOI
10.1016/0370-1573(94)00051-4

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We consider the slave-boson method within the coherent-state functional integral representation of the partition function, and show how to deal with the continuum imaginary-time limit required by the very definition of the functional integral. We find that a correct treatment of the continuum limit modifies the free energy when fluctuation (1/N) corrections beyond the mean-field solution are considered. Numerical results are presented for a two-level single-site model system (with an infinite Hubbard repulsion), for which the additional terms in the free energy introduced by the correct continuum limit act to validate the 1/N expansion. Our analysis calls for a revision of several outcomes of the slave-boson method with the inclusion of fluctuation corrections.
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.