Spin and rotational symmetries in unrestricted Hartree Fock states of quantum dots

TL;DR

This paper investigates the ground states of few-electron quantum dots under magnetic fields using unrestricted Hartree Fock, highlighting symmetry restoration effects, state crossovers, and spin blockade phenomena.

Contribution

It demonstrates how restoring spin and rotational symmetries in Hartree Fock states reveals key physical effects in quantum dots, aligning with more advanced methods.

Findings

Restoring symmetries recovers Hund's first rule.

Ground state crossovers occur with increasing magnetic field.

Spin blockade is confirmed in three and four electron states.

Abstract

Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted Hartree Fock approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons.