Approximate Analytical Dynamical Mean-Field Approach to Strongly Correlated Electron Systems

Abstract

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 selfenergy.

Pseudospin-electron model spectrum in alloy analogy approximation

“…Terms of the R 14 (1)↑ (ω) and R 14 (2)↑ (ω) type are taken into consideration in different ways in various approximations. For example, in Hubbard-III approximation only the first of them is included [5,9]. In this work we use the alloy analogy approximation; in this case terms (64, 65) are neglected (see [9]).…”

Quantum Effects in an Anharmonic Crystal

“…To this end we employ the method already used in the proof of our first theorem. By (42), (36) and (18), one has…”

“…The above formula may be considered as an integro-differential equation with respect to G β,Λ subject to the initial condition (36). By (15), which holds also for the scalar model, to prove the boundedness we need it to be sufficient to control the sequences of the following functions…”

“…Such objects have been studied for many years as quite realistic models of crystalline substance undergoing structural phase transitions [14][15][16]26,27,34,38]. They, and similar models, are also employed as parts of the models describing strong electron-electron correlations caused by the interaction of electrons with vibrating ions [18,35,36]. Starting from the pioneering paper [31], many efforts were made to show that "the more quantum is the model, the less possible is the phase transition".…”

Асимметричная Модель Хаббарда В Методе Производящего Функционала: Спектральные Функции В Пределе Фаликова - Кимбала

“…Однако эти подходы обладают рядом ограничений, и в связи с развитием в последнее время методик расчета электронной структуры на основе метода функционала плотности [18], [19] возникает необходимость разра-ботки новых быстрых алгоритмов. Такими являются, в частности, аналитические аппроксимации для функций Грина [20]- [25].…”