Unrestricted Hartree-Fock for Quantum Dots

TL;DR

This paper demonstrates that Unrestricted Hartree-Fock calculations for quantum dots accurately estimate ground-state energies across various densities, revealing symmetry breaking effects and the transition to Wigner molecule behavior.

Contribution

The study provides a detailed comparison of UHF and RHF methods for quantum dots, highlighting the significance of symmetry breaking and the connection to tight-binding models at strong interactions.

Findings

UHF energies closely match ground-state energies across parameter ranges.

UHF symmetry breaking lowers energy but can mislead density interpretation.

UHF densities show an even-odd effect related to Wigner molecule angular momentum.

Abstract

We present detailed results of Unrestricted Hartree-Fock (UHF) calculations for up to eight electrons in a parabolic quantum dot. The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features. To elucidate the significance of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF) and UHF. While UHF symmetry breaking admits lower ground-state energies, misconceptions in the interpretation of UHF densities are pointed out. An analysis of the orbital energies shows that for very strong interaction the UHF Hamiltonian is equivalent to a tight-binding Hamiltonian. This explains why the UHF energies become nearly spin independent in this regime while the RHF energies do not. The UHF densities display an even-odd effect which is related to the angular momentum of the Wigner molecule. In a weak transversal magnetic field this even-odd effect disappears.