Invariance of the correlation energy at high density and large dimension in two-electron systems

TL;DR

This paper proves that in the high-density, large-dimension limit, the correlation energy of two-electron systems with Coulomb interaction converges to a universal form, explaining similarities observed across different systems.

Contribution

It establishes a universal asymptotic expression for the correlation energy in high-dimensional, high-density two-electron systems with arbitrary radial confinement.

Findings

Correlation energy scales as -1/(8D^2) at large D

Universal behavior explains similarities across various two-electron systems

Results hold for any radial confining potential

Abstract

We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any radial confining potential $V(r)$. This result explains the observed similarity of $\Ec$ in a variety of two-electron systems in three-dimensional space.