On correlation effects in electron spectroscopies and the GW approximation

The GW approximation (GWA) extends the well-known Hartree-Fock approximatio n (HFA) for the self-energy (exchange potential), by replacing the bare Cou lomb potential nu by the dynamically screened potential W, e.g. V-ex = iG n u iis replaced by Sigma(GW) = iGW Mere G is the one-electron Green's functi on. The GWA like the. HFA is self-consistent, which allows for solutions be yond perturbation theory, like say spin-density waves. In a first approxima tion, iGW is a sum of a statically screened exchange potential plus a Coulo mb hole (equal to the electrostatic energy associated with the charge pushe d away around a given electron). The Coulomb hole part is larger in magnitu de, but the two parts give comparable contributions to the dispersion of th e quasiparticle energy. The GWA can be said to describe an electronic polar on (an electron surrounded by an electronic polarization cloud), which has great similarities to the ordinary polaron (an electron surrounded by a clo ud of phonons). The dynamical screening adds new crucial features beyond th e HFA. With the GWA not only bandstructures but also spectral functions can be calculated, as well as charge densities, momentum distributions, and to tal energies. We will discuss the ideas behind the GWA, and generalizations which are necessary to improve on the rather poor GWA satellite structures in the spectral functions. We will further extend the GWA approach to full y describe spectroscopies like photoemission, x-ray absorption, and electro n scattering. Finally we will comment on the relation between the GWA and t heories for strongly correlated electronic systems. In collecting the mater ial for this review, a number of new Results and perspectives became appare nt, which have not been published elsewhere.