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Europhysics Letters (EPL)

New interpolative treatment of the single-impurity Anderson model

G. Czycholl, A. L. Kuzemsky, S. Wermbter

Published Apr 10, 1996• 9 citations
Publisher

Abstract

The many-body quasi-particle dynamics of the single-impurity Anderson model is investigated by means of the equations of motion for the higher-order Green's functions. It is shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently.

DOI
10.1209/epl/i1996-00428-0

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The many-body quasi-particle dynamics of the single-impurity Anderson model is investigated by means of the equations of motion for the higher-order Green's functions. It is shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently.
A new approach to many-body quasiparticle dynamics of the Anderson impurity model at flnite temperatures is proposed in the framework of the equation-of-motion method.We flnd a new exact identity, which relates the one-particle and many-particle Green functions.Using this identity, it is shown that a new interpolating approximation for the one-particle Green function can be constructed.The approximation which simultaneously reproduces tle weak-coupling limit and the strong coupling limit can be formulated self-consistently.This approach offers a new method for a systematic construction of the approximate interpolating dynamical solutions of strongly correlated electron models.
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of chemisorption and adsorbate reactions on metal surfaces, physics of intermediate valence systems, theory of heavy fermions, physics of quantum dots and other nanostructures. While standard treatments are generally based on perturbation methods, our approach is based on the non-perturbative technique for the thermodynamic Green functions. The method of the irreducible Green functions is used as the basic tool. This irreducible Green functions method allows one to describe the quasiparticle spectra with damping of the strongly correlated electron systems in a very general and natural way and to construct the relevant dynamical solution in a self-consistent way on the level of Dyson equation without decoupling the chain of the equations of motion for the Green functions. The subject matter includes the improved interpolating solution of the Anderson model. It was shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently. This approach offers a new way for the systematic construction of approximate interpolation dynamical solutions of strongly correlated electron systems.
The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green’s functions. Using this identity we present a consistent and general scheme for a construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems.
Solving the single-impurity Anderson model is a basic problem of solid state physics.The single-impurity Anderson model is very important, at present it is also used for systems with quantum impurities, e.g.semiconductor quantum dots and molecular transistors.Its main application is in the scheme of dynamical mean eld theory describing strong correlation electron systems.To solve the single-impurity Anderson model problem we use the equation of motion Green function approach.In this report we present the novel equation of motion approximation in which we dierentiate the Green function over both time variables.This diers from the commonly used equation of motion solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable.After extending calculations to higher order Green functions we nd the new approximate dynamical solution of single-impurity Anderson model.The results are compared with the solutions to the single-impurity Anderson model problem at intermediate Coulomb repulsion U such as the modied iterative perturbation theory.Our approach is suitable for describing quantum dots.
The impurity Anderson model with a finite Coulomb repulsion U has been studied by using the conventional equation-of-motion treatment for the f-electron Green's function. To get a closed equation, two types of approximations are incorporated. One is to neglect, in a large U limit, higher order Green's functions which involve three f-electron annihilation operators. The other is to linearize the equation of motion by using a projection operator method. The average valency nf{\mathit{n}}_{\mathit{f}}nf​ and the spectral density of states (DOS) of f electrons are evaluated from the self-consistent equation for the Green's function. Results for nf{\mathit{n}}_{\mathit{f}}nf​ are in good agreement with exact results of Bethe ansatz method, and the obtained spectral DOS exhibits a well-known three-peak structure. Effects of finite U and finite temperature on the spectral DOS are discussed.
The self-consistent theory of the correlation effects in Highly Correlated Systems(HCS) is presented. The novel Irreducible Green's Functions(IGF) method is discused in detail for the Hubbard model and random Hubbard model. The interpolative solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models are discussed briefly.