Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schr\"odinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
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- 1 2 Jing Li,
- 3 N. D. Drummond,
- 2 4 5 Peter Schuck,
- 1 2 6 Valerio Olevano
- 1 Institut Néel [NEEL]
- 2 Universite Grenoblé Alpes / Grenoble Alpes University [UGA]
- 3 Lancaster University
- 4 Institut National de Physique Nucléaire et de Physique des Particules [IN2P3]
- 5 Laboratoire de Physique et Modélisation des Milieux Condensés [LPMMC]
- 6 European Theoretical Spectroscopy Facility [ETSF]