Abstract
Most currently used approximations for the one-particle Green's function G in the framework of many-body perturbation theory, such as Hedin's GW approximation or the cumulant GW+C approach, are based on a linear response approximation for the screened interaction W. The extent to which such a hypothesis is valid and ways to go beyond have been explored only very little. Here we show how to derive a cumulant Green's function beyond linear-response from the equation of motion of the Green's function in a functional derivative formulation. The results can be written in a compact form, which opens the possibility to calculate the corrections in a first principles framework using time-dependent density functional theory. In order to illustrate the potential importance of the corrections, numerical results are presented for a model system with a core level and two valence orbitals.
Highlights
Core-level x-ray photoemission spectroscopy (XPS) is a sensitive probe of correlation properties in condensed matter [1]
As well as the seminal solution of Nozières and De Dominicis [8], trace a way to go towards the inclusion of nonlinear screening effects, these model approaches are not directly transferable to first-principles calculations for several reasons: (i) because of the approximations involved from the very beginning on the interaction potential; (ii) because of the absence of interaction between valence electrons, which would lead to a poor description of screening in the absence of plasmons; and (iii) because it is not clear how an expansion that is order-byorder concerning the response functions would converge
We have demonstrated that the Kadanoff-Baym functional differential equation is a convenient starting point to derive the form of the cumulant Green’s function beyond the linearresponse approximation
Summary
Core-level x-ray photoemission spectroscopy (XPS) is a sensitive probe of correlation properties in condensed matter [1]. In that work the valence electrons that respond to a core-hole excitation are described by an independent-electron picture, and even so, going to yet higher orders turned out to be too complicated While these pioneering works, as well as the seminal solution of Nozières and De Dominicis [8], trace a way to go towards the inclusion of nonlinear screening effects, these model approaches are not directly transferable to first-principles calculations for several reasons: (i) because of the approximations involved from the very beginning on the interaction potential; (ii) because of the absence of interaction between valence electrons, which would lead to a poor description of screening in the absence of plasmons; and (iii) because it is not clear how an expansion that is order-byorder concerning the response functions (i.e., linear response, second-order response, etc.) would converge.
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