Exotic Harmonium Model: Exploring Correlation Effects of Attractive Coulomb Interaction
arXiv:2505.10452 · doi:10.1063/5.0284258
Abstract
Simple few-body systems often serve as theoretical laboratories across various branches of theoretical physics. A prominent example is the two-electron Harmonium model, which has been widely studied over the past three decades to gain insights into the nature of the electron-electron correlations in many-electron quantum systems. Building on our previous work [Phys. Rev. B 108, 245155 (2023)], we introduce an analogous model consisting of an electron and a positively charged particle (PCP) with variable mass, interacting via Coulomb forces while confined by external harmonic potentials. Termed the exotic Harmonium model, this provides insights into the electron-PCP correlations, a cornerstone of the emerging field of the ab initio study of multi-component many-body quantum systems. Through a systematic exploration of the parameter space and numerical solutions of the corresponding Schrödinger equation, we identify two extreme regimes: the atom-like and the particle-in-trap-like behavior. The electron-PCP correlation dominates in the atom-like regime, significantly influencing physical observables, while its role diminishes in the particle-in-trap-like limit. Between these two extremes lies a complex intermediate regime that challenges qualitative interpretation. Overall, the exotic Harmonium model offers a powerful framework to unravel the electron-PCP correlations across diverse systems, spanning particles of varying masses and conditions, from ambient to high-pressure environments.
References in corpus (29)
- Superconducting hydrides under pressure
- Positron-molecule interactions: resonant attachment, annihilation, and bound states
- Development of a Practical Multicomponent Density Functional for Electron-Proton Correlation to Produce Accurate Proton Densities
- Collective and independent-particle motion in two-electron artificial atoms
- Experiment and Theory in Computations of the He Atom Ground State
- Entanglement and density-functional theory: testing approximations on Hooke's atom
- Room Temperature Superconductivity: the Roles of Theory and Materials Design
- Positronium Physics and Biomedical Applications
- Improved generalized gradient approximation for positron states in solids
- Two electrons in an external oscillator potential: hidden algebraic structure
- Nonrelativistic energy levels of helium atom
- Adiabatic connection from accurate wavefunction calculations
- Study of the discontinuity of the exchange-correlation potential in an exactly soluble case
- Correlation energy of two electrons in the high-density limit
- Robust Validation Of Approximate 1-Matrix Functionals With Few-Electron Harmonium Atoms
- Exact Kohn-Sham versus Hartree-Fock in momentum-space: examples of two-fermion systems
- Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes
- Adiabatic connection at negative coupling strengths
- Full correlation single-particle positron potentials for a positron and a positronium interacting with atoms
- Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional
- Exotic atoms
- How Large are Nonadiabatic Effects in Atomic and Diatomic Systems?
- Harmonium as a laboratory for mathematical chemistry
- Ground state of an exciton in a three-dimensional parabolic quantum dot: convergent perturbative calculation
- Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. I. Ground state
- Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system
- Second-order adiabatic connection: The theory and application to two electrons in a parabolic confinement
- Toward a muon-specific electronic structure theory: Effective electronic Hartree-Fock equations for the muonic molecules
- The Pauli Exclusion Operator: example of Hooke's atom