Abstract
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 � 1 � of the single-site Green’s function is constructed in the linear approximation with respect to the coherent potential J�. 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.
Highlights
The lattice models with Hubbard correlations are used in investigating strongly-correlated materials
To systematize and consider a possibility of improving analytic methods we develop the generating functional approach as solver for the single-site problem
Our step is to compare the obtained expression (81) for Ξ−1 with the expression that can be found for the single-site problem of asymmetric Hubbard model (AHM) within the framework of the equation of motion approach using the decoupling [40] used by Jeschke and Kotliar in the paper [23]
Summary
The lattice models with Hubbard correlations are used in investigating strongly-correlated materials. To systematize and consider a possibility of improving analytic methods we develop the generating functional approach as solver for the single-site problem This method is based on the Kadanoff and Baym functional scheme [31] in the form elaborated by Izyumov and Chaschin for the lattice models with strong correlations (for example, Hubbard model and Heisenberg model) [32,33,34,35]. Exemplified by the asymmetric Hubbard model, it is shown that the problem can be formulated as the equation for the Larkin irreducible part Ξ(ω) or the equation for the self-energy and terminal part of the Green’s function This technique allows one to construct an analytic expression for the irreducible part with arbitrary precision in powers of hopping (coherent potential). The generating functional approach enables us to improve these approximations constructing successive iterations for the irreducible part
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