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

Ground state energies are obtained using the unrestricted Hartree Fock (HF) 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's 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 HF 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.