Two-dimensional quantum-dot helium in a magnetic field: Variational theory

TL;DR

This paper introduces a new trial wave function with a Jastrow pair correlation factor for two-electron quantum dots in magnetic fields, demonstrating its accuracy across all field strengths through comparison with numerical results.

Contribution

The paper proposes a novel variational wave function with a displaced Gaussian Jastrow factor for 2D quantum-dot helium in magnetic fields, validated against numerical diagonalization.

Findings

The trial wave function accurately represents the ground state at all magnetic field strengths.

It maintains high quality from zero to strong magnetic fields.

Comparison with numerical results confirms its effectiveness.

Abstract

A trial wave function for two-dimensional quantum dot helium in an arbitrary perpendicular magnetic field (a system of two interacting electrons in a two-dimensional parabolic confinement potential) is introduced. A key ingredient of this trial wave function is a Jastrow pair correlation factor that has a displaced Gaussian form. The above choice of the pair correlation factor is instrumental on assuring the overall quality of the wave function at all values of the magnetic field.Exact numerical diagonalization results are used to gauge the quality of the proposed trial wave function.We find out that this trial wave function is an excellent representation of the true ground state at all values of the magnetic field including weak (or zero) and strong magnetic fields.