Self-interaction in Green's-function theory of the hydrogen atom

TL;DR

This paper investigates self-interaction errors in the GW approximation of many-body perturbation theory using atomic hydrogen as a benchmark, highlighting the small but non-zero self-interaction contributions.

Contribution

It provides a detailed analysis of self-interaction effects in GW calculations for hydrogen, emphasizing the differences between using exact and approximate wavefunctions.

Findings

Self-interaction in GW is small but non-zero for hydrogen.

Exact wavefunctions reduce self-interaction errors compared to LDA.

Hydrogen serves as an effective benchmark for GW self-energy accuracy.

Abstract

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.