Many-body perturbation theory and non-perturbative approaches: the screened interaction as key ingredient

TL;DR

This paper investigates the effectiveness of different levels of approximation in many-body perturbation theory, emphasizing the importance of the screened interaction, and proposes promising nonperturbative approaches based on a simplified model.

Contribution

It analyzes various screening approximations within many-body perturbation theory using a zero-dimensional model, highlighting the potential of RPA screening and nonperturbative solutions.

Findings

RPA screening expansion is most promising for real systems.

Nonperturbative solutions from Kadanoff-Baym equations show potential.

Different screening levels significantly impact the accuracy of many-body calculations.

Abstract

Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Green's function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called 'one-point model') that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff-Baym equation for the one-body Green's function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.