  Enlarged symmetry characterized by the group SU(4) can be realized in
isolated semiconducting quantum dots. A Hubbard model then describes a pillar
array of coupled dots and at half-filling the system can be mapped onto an
SU(4) spin chain. The physics of these new structures is rich as novel phases
are attainable. The spins spontaneously dimerize and, by using the Density
Matrix Renormalization Group (DMRG), we show that the dimer state is robust to
perturbations which break SU(4) symmetry. We propose ways to experimentally
verify the existence of the dimerized phase.
