Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

TL;DR

This paper evaluates the accuracy of the Hartree-Fock method for modeling Wigner molecules in high magnetic fields, comparing it with exact solutions to understand its limitations and the role of symmetry in charge density distributions.

Contribution

It introduces a generalized multicenter Gaussian basis for Hartree-Fock calculations and analyzes the method's accuracy at high magnetic fields for few-electron quantum dot systems.

Findings

HF energy estimates become exact at infinite magnetic fields

Broken-symmetry HF solutions match classical charge distributions in high fields

Symmetry considerations influence HF accuracy in Wigner molecule modeling

Abstract

Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact results allows us to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution can be identified with the classical charge distribution.