Two-electron entanglement in a two-dimensional isotropic harmonic trap: Radial correlation effects in the low density limit

TL;DR

This paper investigates the entanglement properties of two electrons in a 2D harmonic trap, focusing on radial correlation effects at low density and strong interaction limits, revealing asymptotic independence of angular and radial correlations.

Contribution

It provides the first quantitative analysis of pure radial correlation effects in a two-electron 2D system at strong interaction limits.

Findings

Entanglement depends on interaction strength

Angular and radial correlations become independent at strong interactions

Radial correlation effects are quantitatively characterized

Abstract

We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the degeneracy in the spectrum of the reduced density matrix and provide detailed results for the dependencies of the entanglement on the interaction strength. Among other features, it is indicated that in the limit of an infinitely strong interaction, the angular and radial correlations are asymptotically independent of each other. Appearing in this limit, the pure radial correlation effects are quantitatively investigated for the first time.