Nonlinear response in the cumulant expansion for core-level photoemission

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.

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

“…2(c) and (e) that both the Dyson's approach and the cumulant approach exhibit satellites states. As already discussed in numerous reports, 25,[29][30][31][34][35][36][37][38][40][41][42][43]45,46,[66][67][68][69][70][71] Dyson's approach yields only one satellite, to leading order located at a binding energy of (1 + α) ω 0 from the QP peak, see Fig. 2(c).…”

“…A promising strategy to include higher-order electronphonon diagrams beyond the Fan-Migdal self-energy is provided by the cumulant expansion formalism. 19,25,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] Owing to its roots in the description of deep-lying core states, the cumulant is a priori defined in terms of the lesser and greater self-energy, clearly separating electron and hole states. Later adaptations to states near the Fermi level include the introduction of the retarded cumulant.…”

“…34 More recently, the cumulant approach has been employed to improve the description of spectral satellites arising from electron-plasmon interactions in GW calculations. [35][36][37][38][39][40][41][42][43] In the context of electron-phonon physics, the cumulant expansion has successfully been employed to calculate phonon sidebands in systems exhibiting Fröhlich coupling. 19,25,[29][30][31][44][45][46] Despite much progress on the front of ab initio calculations, we still lack a simple analytical model that captures the essential features of Fröhlich interactions in doped systems, and that can be used as a reference benchmark for validating ab initio implementations.…”

Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-Ray Spectra

“…The most common approximation is to expand the Green’s function to low order either in the bare Coulomb interaction, giving β ( ω ) in terms of the second order self-energy ( Vila et al, 2020 ), or by expanding in terms of the screened Coulomb interaction, which produces an approximation in terms of the GW self-energy ( Hedin, 1999 ; Guzzo et al, 2011 ; Zhou et al, 2015 ). Approximate non-linear corrections can be included using real-time TDDFT ( Tzavala et al, 2020 ). Here, as described in the next section, we calculate the cumulant including non-linear corrections within a non-perturbative approach, by expressing the Green’s function in terms of the time-dependent EOM-CC states.…”

Ab initio multiplet plus cumulant approach for correlation effects in x-ray photoelectron spectroscopy

“…Computational schemes that combine these aspects are highly desirable for strongly correlated materials such as transition metal oxides (TMOs). This is the main goal of this work, where a local LFMT model is combined with the non-linear cumulant Green's function approach [10][11][12][13] to treat both local-and longerrange correlated behavior.…”