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

Abstract

Helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger 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.

6 pages, 2 figures, 3 tables

References in corpus (1)

• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications

Cited by in corpus (15)

• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Ab Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals
• Excitonic structure of the optical conductivity in MoS${}_2$ monolayers
• Connections and performances of Green's function methods for charged and neutral excitations
• Unphysical Discontinuities in GW Methods
• Green functions and self-consistency: insights from the spherium model
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• A similarity renormalization group approach to Green's function methods
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Comparing many-body approaches against the helium atom exact solution
• A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW +BSE and self-consistent RPA
• Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches
• Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature