## Comparing many-body approaches against the helium atom exact solution

Jing Li, N. D. Drummond, Peter Schuck, Valerio Olevano

SciPost Phys. 6, 040 (2019) · published 1 April 2019

- doi: 10.21468/SciPostPhys.6.4.040
- Submissions/Reports

### Abstract

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.

### Cited by 19

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Jing Li, -
^{3}N. D. Drummond, -
^{2}^{4}^{5}Peter Schuck, -
^{1}^{2}^{6}Valerio Olevano

^{1}Université Grenoble Alpes / Grenoble Alpes University [UGA]^{2}Institut Néel [NEEL]^{3}Lancaster University^{4}Laboratoire de Physique et Modélisation des Milieux Condensés [LPMMC]^{5}Institut National de Physique Nucléaire et de Physique des Particules [IN2P3]^{6}European Theoretical Spectroscopy Facility [ETSF]