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International Journal of Modern Physics B

BETHE APPROXIMATION SCHEME FOR ITINERANT ELECTRON SYSTEMS

MARIA BECHI, Roberto Livi, Arianna Montorsi

Published Nov 10, 1991• 0 citations
Publisher

Abstract

After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.

DOI
10.1142/s0217979291001164

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The authors propose an alternative interpretation of the Fermi linearization approach to interacting electron systems, based on the requirement that the coefficients of the linearized operators are Clifford-like variables, whose anticommutator equals an unknown constant c. They apply the approximation to the Falicov-Kimball model (1969), explicitly solving the self-consistency equation for the unknown, which turns out to behave as an order parameter. They discuss its relation with a metal-insulator transition and some thermodynamical quantities. In particular they show that the approximation in the T=0 limit reproduces exactly the Gutzwiller results (1965) for the Hubbard model.
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Within the binary, self-consistent static approximation to the Hubbard-model, local moments are created out of itinerant electrons. The magnetic Ising-type interactions of these local moments are calculated and explicit results are obtained. Relaxing the static character of the approximation transforms the interactions to Heisenberg type and renormalises their size. Renormalisation is necessary in order to satisfy certain sum rules. The authors' results are in good agreement with exact many-body results.