Comparing many-body approaches against the helium atom exact solution

Jing Li1,2, N. D. Drummond3, Peter Schuck1,4,5and Valerio Olevano1,2,6?

 

 Abstract

 Over time, many different theories and approaches have been developed to tackle themany-body problem in quantum chemistry, condensed-matter physics, and nuclearphysics. Here we use the helium atom, a real system rather than a model, and we usethe exact solution of its Schrödinger equation as a benchmark for comparison betweenmethods. We present new results beyond the random-phase approximation (RPA) from arenormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originallydeveloped in nuclear physics, and compare them with various other approaches likeconfiguration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of theGWapprox-imation. Most of the calculations are consistently done on the same footing, e.g. usingthe same basis set, in an effort for a most faithful comparison between methods.

 

https://scipost.org/SciPostPhys.6.4.040/pdf