Higher order many-body perturbation theory applied to atomic systems*

While the GW method has been the subject of an intense work of validation, higher-order many-body perturbation theory (MBPT) methods have received much less attention. Here we investigate the performance of beyond-GW MBPT approaches in atomic systems described within the spherical approximation. By using a dedicated numerical treatment based on a B-spline/spherical harmonics representation [1], we obtain benchmark results avoiding many commonly adopted approximate procedures (including complete basis set extrapolations, and frequency description). We present a variety of results, including static polarizabilities, ionization potentials, and Kohn-Sham exchange and correlation potentials as obtained from the solution of the Sham-Schlüter equation (SSE) for a number of MBPT schemes, including GW, 2nd Born, and SOSEX [2] self-energies.
[1] M. Hellgren and U. von Barth, Phys. Rev. B 76, 075107 (2007).
[2] X. Ren et al., Phys. Rev. B 92, 081104 (2015).