Expansão em cumulantes para o Modelo de Anderson Periodico

AUTOR(ES)
DATA DE PUBLICAÇÃO

1994

RESUMO

The diagrammatic expansion in cumulants that was employed by Hubbard to study his model of a narrow band of strongly correlated electrons was extended to the Periodic Anderson Model (PAM). The model was also extended by considering localized electronic states with an arbitrary scheme of energy levels: this extension would be useful to study intermediate valence compounds of Eu or Tm with the present formalism. The rules for the diagrammatic calculation of the grand canonical potential and of the Green s functions (GF) for the general model have been derived: only connected diagrams appear in those calculations, and the lattice sums are unrestricted. To generate the cumulant averages it was necessary to employ external fields x that are Grassman variables and it is presented a simple way to extend the diagrammatic rules for the x ¹ 0 case. The cumulant expansion was applied to the P AM for a wide rectangular band of conduction electrons (wide band) and for a conduction band of zero width (atomic limit), in the case of an infinite repulsion between two localized electrons at the same site (U = ¥). Two different families of diagrams were considered to calculate the one-particle GF in the paramagnetic phase: 1) the chain approximation (CHA) employing only second order cumulants, 2) the multiple loop approximation (MLA), that also considers rings of all sizes, but employs at most fourth order cumulants. The occupation numbers per site and per spin of the localized electrons (nf) and of the conduction electrons (nc) are obtained from the GF, and the lack of completeness in the space of localized electrons and the non-analyticity of the GF off the real axis are discussed: new approaches to treat these two problems are presented. The F-derivable approximations were also employed. It was possible to show that CHA is a F-derivable approximation, in which the only approximation is the choice of the diagrams employed to calculate the functional F , from which the GF can be obtained. It was then clear that the F-derivable approximations do not solve the lack of completeness. We have also studied a F-derivable extension of the MLA, but in this case it was necessary to add a further approximation, namely to restrict the cumulants employed to fourth order only. In this last case the numerical calculations were only performed in the atomic limit, because the wide band case would require a rather long time of computation, and from the results in the atomic limit we did not expect that this approximation would solve the completeness problem. In the final stages of the present work a technique that solve the completeness problem in a context of X Hubbard operators was discovered. A general conjecture, that has been verified in alI the cases we considered, is presented. The numerical results for two of these approximations, both for the wide band and for the atomic limit, are given

ASSUNTO(S)

mecanica quantica green modelo de hubbard funções de

ACESSO AO ARTIGO

Documentos Relacionados