  Classes of spontaneous symmetry breaking at zero and low magnetic fields in
single quantum dots (QD's) and quantum dot molecules (QDM's) are discussed in
relation to the ratio R_W between the interelectron Coulomb repulsion and the
harmonic confinement, using spin-and-Space unrestricted Hartree-Fock
calculations. These include: Wigner crystallization for R_W > 1, and formation
of non-crystallized electron puddles localized on the individual dots in QDM's,
as well as spin-density waves in single QD's, for R_W < 1.
  Erratum:
  Subsequent to the the publication of our Letter, we have performed further
systematic spin-and-space unrestricted Hartree-Fock calculations. While the
behavior and magnitudes of the addition energies shown in our Letter are
maintained, as well as our finding pertaining to the prevalent violation of
Hund's first rule, our improved calculations yield in certain instances
different spin polarizations.
