Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation

TL;DR

This paper introduces an iterative method to improve the electron self-energy calculations by solving Hedin's equations beyond the GW approximation, demonstrating convergence and improved accuracy.

Contribution

It provides a systematic procedure for deriving more accurate vertex corrections through iterative solutions of Hedin's equations, extending beyond the GW approximation.

Findings

Convergence of the iterative process demonstrated with Hubbard Hamiltonian

Explicit formula for the vertex function from the second cycle

Calculated excitation energies support the GW approximation's validity

Abstract

We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the GW approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the GW approximation.