Abstract
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.
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