  Optical lattices are considered loaded by atoms or molecules that can exhibit
strong interactions between different lattice sites. The strength of these
interactions can be sufficient for generating collective phonon excitations
above the ground-state energy level. Varying the interaction strength makes it
possible to create several equilibrium three-dimensional phases, including
conducting optical lattices, insulating optical lattices, delocalized quantum
crystals, and localized quantum crystals. Also, there can exist finite one- and
two-dimensional lattices of chains and planes.
