Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function

Abstract

A new cumulant-based GW approximation for the retarded one-particle Green's function is proposed, motivated by an exact relation between the improper Dyson self-energy and the cumulant generating function. Qualitative aspects of this method are explored within a simple one-electron independent phonon model, where it is seen that the method preserves the energy moment of the spectral weight while also reproducing the exact Green's function in the weak coupling limit. For the three-dimensional electron gas, this method predicts multiple satellites at the bottom of the band, albeit with inaccurate peak spacing. However, its quasiparticle properties and correlation energies are more accurate than both previous cumulant methods and standard G 0 W 0 . Our results point to new features that may be exploited within the framework of cumulant-based methods and suggest promising directions for future exploration and improvement of cumulant-based GW approaches.

Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals

“…It was then proposed that self-energy (SE) diagrams with vertex corrections may cancel the spurious SC effects [25,[30][31][32][33]. This fueled a number of notable attempts to include the vertex function in a model fashion: using the plasmon model for the screened interaction [34], neglecting the incoherent part of the electron spectral function [35], and employing the Ward identities and a model form of the exchange-correlation kernel [27,[36][37][38], or the cumulant expansions [39][40][41][42][43][44][45]. Although these methods clarified a number of issues, they do not provide an exhaustive picture [46].…”

One-electron spectra and susceptibilities of the three-dimensional electron gas from self-consistent solutions of Hedin's equations

“…Plasmon satellites in electron gas have been studied recently using the positive-definite diagrammatic expansion for the spectral function 14 and the GW+Cumulant approach. [33][34][35][36] Both methods are implemented on real frequency axis and, thus, do not involve analytical continuation as an intermediate step in evaluating the spectral function. In these works, very good agreement with the experimental position of plasmon satellite in Na has been achieved.…”

Dynamically screened vertex correction to GW

“…Other diagrams, for instance cc , are important for the off-shell spectroscopic properties, e.g., second plasmonic satellites [8,10,32,35]. Dedicated methods based on the cumulant expansion [33,34,37,38] can describe them at the reduced numerical cost. The very fact that different diagrams are operative in distinct spectral ranges [6,29] and contribute additively to the scattering rate (k, ω) makes it possible to separately consider these effects.…”

“…have been directed to extend the method towards the valence states [33,34], plasmonic satellites have been observed [8,35] and predicted [36] in a wide range of realistic systems and in the homogeneous electron gas [37,38].…”