Comparing many-body approaches against the helium atom exact solution

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 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.

arXiv comment23 pages, 9 figures, 11 tables

References in corpus (19)

• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Continuum variational and diffusion quantum Monte Carlo calculations
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• Jastrow correlation factor for atoms, molecules, and solids
• Reference Energies for Double Excitations
• Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
• Experiment and Theory in Computations of the He Atom Ground State
• Fine structure of helium-like ions and determination of the fine structure constant
• Nonrelativistic ionization energy for the helium ground state
• Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas
• The momentum distribution of the homogeneous electron gas
• Efficient ab initio calculations of bound and continuum excitons
• Vertex corrections in localized and extended systems
• Green functions and self-consistency: insights from the spherium model
• How Large is the Elephant in the Density Functional Theory Room?
• Progress in Many Body Theory with the Equation of Motion method. Time dependent Density Matrix meets Self-Consistent RPA. Applications to solvable Models
• Helium atom excitations by the GW and Bethe-Salpeter many-body formalism
• Momentum distribution and Compton profile by the ab initio GW approximation
• Self-Consistent RPA from a Coupled Cluster Wave Function Perspective

Cited by in corpus (14)

• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Connections and performances of Green's function methods for charged and neutral excitations
• Accurate atomic correlation and total energies for correlation consistent effective core potentials
• Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies
• A similarity renormalization group approach to Green's function methods
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• Scrutinizing $GW$-based methods using the Hubbard dimer
• RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods
• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• A first step in the nuclear inverse Kohn-Sham problem: from densities to potentials
• Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation
• Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches
• Self-Consistent Random Phase Approximation from Projective Truncation Approximation Formalism