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 Schrödinger 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 \boldsymbol{GW}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.
Highlights
IntroductionThe neutral helium atom and other two-electron ionized atoms are among the simplest manybody systems in nature
Our work presented a comparison on the same footing, in particular using the same Gaussian basis set, of several many-body approaches, including a not so much explored renormalized random-phase approximation (RPA) (r-RPA) derived from the equation of motion (EOM) method developed in nuclear physics
Our work shows that the r-RPA, which is a sub-product of the self-consistent RPA (SCRPA) approach, improves over the standard RPA (i.e. linearized time-dependent Hartree-Fock (TDHF) [33]) and achieves a result of accuracy comparable to GW +Bethe-Salpeter equation (BSE), except for the first excited state where there is no improvement
Summary
The neutral helium atom and other two-electron ionized atoms are among the simplest manybody systems in nature. In order to compare with the other approaches, we at the same time calculate helium ground and excited states by some of the most widespread many-body approaches, including Hartree-Fock (HF), quantum Monte Carlo (QMC), quantum chemistry configuration interaction (CI), density-functional theory (DFT) and time-dependent density-functional theory (TDDFT), Bethe-Salpeter equation (BSE) [18,19,20] on top of the GW approximation [21,22,23,24,25], and the dRPA approximation on top again of the GW electronic structure, or of the HF or the DFT ones (see Fig. 1) Some of these results were previously presented in the literature, but here we made the effort to recalculate most of them on the same footing, in particular using the same Gaussian basis set, which, as we will see, significantly affects the accuracy of the results. The zero of the energies will be fixed at the helium atom double excitation level He++ + 2e− when studying the helium ground state, and at the ground state 11S when studying the excitation spectrum
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