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Physica B Condensed Matter

Exact results for the Anderson model in the limit of zero-width conduction band

Francesco Paolo Mancini, M. Marinaro, Y. Nakano

Published Sep 1, 1989• 14 citations
Publisher
DOI
10.1016/0921-4526(89)90013-6

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The previously derived variational-derivative equations for the Hubbard model and for the single-impurity Anderson model after the Legendre transformation are represented in the form of a set of two nonlinear integral equations. The one-particle propagators of the number of particles and of the momentum that are defined by these equations exhibit a regular behavior in three limiting cases. First, for both models in the limit of the zero width of the conduction band (W/U = 0) there is obtained a result known as the atomic limit. Second, it has been shown that in the limit of U/W ≪ 1 the Pauli principle in the form of an additional coupling equation excludes from the perturbation-theory series some class of diagrams that are present in the standard expansion. Finally, for the case of U = ∞ and N e = N at − 1 in the framework of the Hubbard model there has been obtained an equation that agrees with the exact Nagaoka statement on the saturated ferromagnetism. A calculation has been performed of the density of impurity electron states in the symmetrical Anderson model in the paramagnetic phase for various values of the parameters of the Coulomb interaction U/πΓ and temperature T/Γ, where Γ is the width of the localized impurity level. The calculation results are in good agreement with the results obtained by other methods.
The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion is considered here for an hypercubic lattice of infinite dimension . The nearest neighbour hopping of the uncorrelated electrons is described exactly by a conduction band, while two different models of hybridization are treated as a perturbation. The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of , are also shown to be valid for the periodic Anderson model. The derivation of these properties had to be modified because of the exact treatment of the conduction band.