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arXiv:cond-mat/0504723 · The European Physical Journal B

A generating functional approach to the Hubbard model

Yu. A. Izyumov, N. I. Chaschin, D. S. Alexeev, F. Mancini

Published May 1, 2005• 15 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2005-00166-7

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The method of a generating functional of Green’s functions was further developed within the framework of the Hubbard model and single-impurity Anderson model. In contrast to the earlier proposed works, the equations in the variational derivatives for the partition functions are presented here in the closed form, i.e. the role of variables is played by the physical matrix parameters of the systems rather than by the external local fluctuating fields. The solutions to these equations are the generating functionals of different Green’s functions. It is shown that the simplest iterative solutions in terms of the parameters U / W and W / U in the case of the Hubbard model or U /Δ and Δ/ U for the Anderson model, where U is the Coulomb repulsion on a site, W is the width of a free electron zone, and Δ is the width of an impurity level, lead to the well-known results of the weak and strong coupling limits.
In the paper a new analytic approach to the solution of the effective single-site problem in the dynamical mean field theory is developed.The approach is based on the method of the Kadanoff-Baym generating functional in the form developed by Izyumov et al.It makes it possible to obtain a closed equation in functional derivatives for the irreducible part of the single-site particle Green's function; the solution is constructed iteratively.As an application of the proposed approach the asymmetric Hubbard model (AHM) is considered.The inverse irreducible part Ξ -1 σ of the single-site Green's function is constructed in the linear approximation with respect to the coherent potential Jσ.Basing on the obtained result, the Green's function of itinerant particles in the Falicov-Kimball limit of AHM is considered, and the decoupling schemes in the equations of motion approach (GH3 approximation, decoupling by Jeschke and Kotliar) are analysed.