Arxiv:1801.09977V3 [Physics.Atom-Ph] 1 Mar 2019 10 Helium
Comparing many-body approaches against the helium atom exact solution Jing Li,1, 2 N. D. Drummond,3 Peter Schuck,1, 4, 5 and Valerio Olevano1, 2, 6, ∗ 1Universit´eGrenoble Alpes, 38000 Grenoble, France 2CNRS, Institut N´eel, 38042 Grenoble, France 3Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom 4CNRS, LPMMC, 38042 Grenoble, France 5CNRS, Institut de Physique Nucl´eaire, IN2P3, Universit´e Paris-Sud, 91406 Orsay, France 6European Theoretical Spectroscopy Facility (ETSF) (Dated: March 4, 2019) 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. I. INTRODUCTION did not yet exist. It played a fundamental role in as- sessing the validity of quantum mechanics as a universal The neutral helium atom and other two-electron ion- theory that does not just apply to the hydrogen atom.
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