Beyond the GW approximation: combining correlation channels

TL;DR

This paper develops a unified framework combining the GW approximation and T-matrix methods in many-body perturbation theory to better describe electron correlations across different density regimes.

Contribution

It derives a common framework linking GW and T-matrix approaches, clarifying their relationship and enabling improved correlation descriptions in MBPT.

Findings

Unified derivation of T-matrix and GW methods

Clarification of electron-hole and particle-particle T matrices

Application to the Hubbard molecule demonstrating the approach

Abstract

In many-body perturbation theory (MBPT) the self-energy \Sigma=iGW\Gamma plays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex function \Gamma to unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the T matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT we show how one can derive the T-matrix approximation to the self-energy in a common framework with GW. This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle T matrix, the derivation of a screened T matrix, and the conversion of the T matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration.