Electronic Dynamics of the Anderson Model. The Many-Body Approach

TL;DR

This paper reviews the electronic dynamics of Anderson models using a non-perturbative Green functions approach, providing a self-consistent interpolating solution that captures both weak and strong coupling regimes.

Contribution

It introduces a self-consistent, non-perturbative Green functions method for Anderson models, enabling accurate interpolation between different coupling limits.

Findings

Developed a self-consistent interpolating approximation for the Anderson model.

Reproduces weak and strong coupling limits up to second order.

Provides a systematic way to construct dynamical solutions for strongly correlated systems.

Abstract

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.