Exotic Harmonium Model: Exploring Correlation Effects of Attractive Coulomb Interaction

TL;DR

The paper introduces the exotic Harmonium model, a two-particle Coulomb-interacting system with variable mass, to study electron-positively charged particle correlations across different regimes, revealing complex intermediate behaviors.

Contribution

It extends the traditional Harmonium model to include a variable-mass positively charged particle, providing new insights into multi-component quantum correlations.

Findings

Identification of atom-like and particle-in-trap-like regimes

Dominance of electron-PCP correlation in the atom-like regime

Complex intermediate regime with challenging interpretation

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 Schr\"odinger 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.