Variational solution of the T-matrix integral equation

TL;DR

This paper introduces a variational approach to solving the T-matrix integral equation with a local approximation, linking it to local-field factors and proposing a new form for electron self-energy calculations that avoids double counting.

Contribution

It presents a novel variational solution to the T-matrix integral equation incorporating local interactions dependent on momentum and frequency, improving electron self-energy modeling.

Findings

Derived a simple T-matrix form similar to Hubbard models

Connected local interaction to local-field factors

Proposed a double-counting-free T-matrix contribution to self-energy

Abstract

We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and frequency. By examining the ladder diagrams for irreducible polarizability, a connection between this interaction and the local-field factor is established. Based on the obtained solution, a form for the T-matrix contribution to the electron self-energy in addition to the GW term is proposed. In the case of the electron-hole multiple scattering, this form allows one to avoid double counting.