Approximate analytical dynamical mean-ﬁeld approach to strongly correlated electron systems - Stasyuk, I.V. (Condensed Matter Physics, 2000)
An approximate analytical scheme of the dynamical mean-ﬁeld theory (DMFT), that is used for electron systems with Hubbard correlations and is exact in the limit of the inﬁnite dimensionality of a space, is developed. The effective single-site problem arising in the framework of this method is formulated in terms of the auxiliary Fermi-ﬁeld. The irreducible Green's function technique with the projecting on the Hubbard basis of Fermi-operators is used for its solution. A system of DMFT equations is obtained in the approximation which is a generalization of the Hubbard-III approximation and combines it with a self-consistent renormalization of the local electron levels. It is shown that the proposed approach includes as simple speciﬁc cases a number of known approximations (Hubbard-III, AA, MAA, . . . ) based on the assumption of the single-site structure of the electron self- energy.