arXiv:cond-mat/9807353 · Journal of Physical Studies

Pseudospin-electron model in infinite dimensions

Ihor V. Stasyuk, Andrij M. Shvaika

Published Jan 1, 1999• 8 citations

Abstract

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.

DOI: 10.30970/jps.03.177

Related papers

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

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.

arXiv:cond-mat/9811019Nov 2, 19980 citations

Energy spectrum of pseudospin-electron model in the dynamical mean-field theory

Ihor V. Stasyuk, Володимир Олександрович Краснов

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.

arXiv:1302.1404Feb 6, 20130 citations

Dynamical susceptibilities in the strong coupling approach: A general scheme and the Falicov–Kimball model

Andrij M. Shvaika

A general scheme to calculate dynamical susceptibilities of strongly correlated electron systems within the dynamical mean eld theory is developed.The approach is based on an expansion over electron hopping around the atomic limit (within the diagrammatic technique for site operators: projection and Hubbard ones) in in nite dimensions.As an example, the Falicov{Kimball and simpli ed pseudospin-electron models are considered for which an analytical expressions for dynamical susceptibilities are obtained.

arXiv:cond-mat/0203492Journal of Physical StudiesJan 1, 200115 citations

The ground state problem in the infinite-U Hubbard model

E. V. Kuz’min

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.

Physics of the Solid StateFeb 1, 19973 citations

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Antoine Georges, Gabriel Kotliar, Werner Krauth +1 more

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Reviews of Modern PhysicsJan 1, 19966,900 citations

From the atomic limit to a metal-insulator transition in the Hubbard model

L. Craco, M. A. Gusmão

Starting from the exact solution of the Hubbard model in the atomic limit, and treating the hopping term as a perturbation by means of a diagram technique, we discuss the electronic structure of the model in some simple approximations. We show that a metal-insulator transition is obtained above a critical value of the on-site Coulomb interaction in a self-consistent evaluation of the one-particle Green's function to one-loop order. A relationship with results in infinite dimensions is briefly discussed.

Physical review. B, Condensed matterDec 15, 199527 citations