Exact broken-symmetry states and Hartree-Fock solutions for quantum dots at high magnetic fields

TL;DR

This paper compares exact diagonalization and unrestricted Hartree-Fock methods in studying high magnetic field Wigner molecules in quantum dots, revealing differences in charge localization and symmetry breaking.

Contribution

It provides a detailed comparison between ED and UHF approaches for broken-symmetry states in quantum dots at high magnetic fields, highlighting limitations of UHF.

Findings

UHF overestimates charge localization compared to ED.

Broken-symmetry states can be constructed from ED solutions.

UHF neglects dependence of wave functions on electron positions.

Abstract

Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave function on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states.