Helium atom excitations by the GW and Bethe-Salpeter many-body formalism

TL;DR

This paper evaluates the accuracy of the GW and Bethe-Salpeter many-body formalism for helium atom excitations, demonstrating their high precision and comparing them to other methods like TDDFT.

Contribution

It provides a detailed ab initio assessment of GW and BSE methods against exact solutions for helium, highlighting their accuracy in a simple many-electron system.

Findings

GW and BSE yield highly accurate excitation energies and oscillator strengths.

Results outperform time-dependent Hartree-Fock systematically.

Self-interaction and self-screening issues are not significantly limiting in helium.

Abstract

Helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schr\"odinger equation is known for helium ground and excited states, and represents a workbench for any many-body methodology. Here, we check the ab initio many-body GW approximation and Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from Hartree-Fock, we show that GW and BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving time-dependent Hartree-Fock. These findings suggest that the accuracy of BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.