Comparing many-body approaches against the helium atom exact solution

TL;DR

This paper benchmarks various many-body computational methods against the exact solution of the helium atom, introducing a new renormalized RPA approach and comparing it with established techniques.

Contribution

It introduces a renormalized RPA method within SCRPA and provides a comprehensive comparison with other approaches using a consistent basis set.

Findings

r-RPA improves upon standard RPA results

Comparison shows varying accuracy of methods against exact solution

Most methods are evaluated on equal footing for fair comparison

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.