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

TL;DR

This paper introduces a new cumulant-based $GW$ approximation for the retarded Green's function, improving the accuracy of quasiparticle and satellite property predictions in many-electron systems.

Contribution

It proposes a novel cumulant approach linked to the Dyson self-energy, enhancing the description of satellite features and quasiparticle energies in electronic structure calculations.

Findings

Preserves spectral weight energy moments.

Reproduces exact Green's function in weak coupling.

Predicts multiple satellites with improved quasiparticle energies.

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 $G_0W_0$. 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.