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arXiv:cond-mat/9811019

Dynamics and thermodynamics of the pseudospin-electron model in the case of absence of the electron Hubbard correlation. I. The analytical consideration

Ihor V. Stasyuk, Andrij M. Shvaika, K. V. Tabunschyk

Published Nov 2, 1998• 0 citations
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Abstract

Dynamics and thermodynamics of the model with local anharmonism in the case of absence of the electron (Hubbard) correlation is investigated in the present work. The correlation functions, mean values of pseudospin and particle number as well as the thermodynamical potential are calculated. The calculation is performed by diagrammatic method in the mean field approximation. Single--particle Green functions are taken in the Hubbard--I approximation.

DOI
10.48550/arxiv.cond-mat/9811019

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Dynamics and thermodynamics of the model with local anharmonism in the case of absence of the electron (Hubbard) correlation is investigated in the present work. The correlation functions, mean values of pseudospin and particle number as well as the thermodynamical potential are calculated. The calculation is performed by diagrammatic method in the mean field approximation. Single--particle Green functions are taken in the Hubbard--I approximation.
Energy spectrum and thermodynamics of the pseudospin{electron model are investigated in the dynamical mean eld approximation (d = 1 limit).In the limit of zero electron correlation this model is analytically exactly soluble within this approach: in the = const regime the rst order phase transition with the jump of the pseudospin mean value and reconstruction of the electron spectrum can be realized, while in the n = const regime the phase separation in electron subsystem can take place for certain values of the model parameters.On the basis of the obtained results the applicability of the approximate schemes previously used for the investigation of the pseudospin{ electron model are discussed.
A method of consideration of gaussian fluctuations of the effective mean field within the framework of the GRPA scheme is applied to investigation of thermodynamical properties of a pseudospin-electron model (PEM). The grand canonical potential, pseudospin mean value, as well as the mean squares of fluctuations are calculated. Obtained results are compared with corresponding ones obtained by other approximations. An influence of the gaussian fluctuations of mean field on the thermodynamic properties of PEM is discussed.
The pseudospin-electron model in the case of infinite on-site electron repulsion is investigated. The electron energy spectrum is calculated within the framework of the dynamical mean field theory (DMFT), and the alloy analogy approximation is developed. The effect of the pseudospin-electron interaction, local asymmetry field, and tunneling-like level splitting on the existence and the number of electron subbands is investigated. The relation of the pseudospin-electron model to the problem of energy spectrum of boson-fermion mixtures in optical lattices is discussed.
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.
Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential, one-particle propagator and correlation function is established. This relation contains additional integration of the one-particle propagator by the auxiliary constant. The vacuum skeleton diagrams constructed from irreducible Green’s functions and tunneling propagator lines are determined and special functional is introduced. The properties of such functional are investigated and its relation to the thermodynamic potential is established. The stationary properties of this functional with respect to first order changing of the correlation function is demonstrated and as a consequence the stationary properties of the thermodynamic potential is proved.
The asymmetric Hubbard model is used in investigating the lattice gas of the moving particles of two types.The model is considered within the dynamical mean-field method.The effective single-site problem is formulated in terms of the auxiliary Fermi-field.To solve the problem an approximate analytical method based on the irreducible Green's function technique is used.This approach is tested on the Falicov-Kimball limit (when the mobility of ions of either type is infinitesimally small) of the infinite-U case of the model considered.The dependence of chemical potentials on concentration is calculated using the one-particle Green's functions, and different approximations are compared with the exact results obtained thermodynamically.The densities of states of localized particles are obtained for different temperatures and particle concentrations.The phase transitions are investigated for the case of the Falicov-Kimball limit in different thermodynamic regimes.