Abstract
Double-well optical lattice in an insulating state is considered. The influence of atomic vibrations and mesoscopic disorder on the properties of the lattice are studied. Vibrations lead to the renormalization of atomic interactions. The occurrence of mesoscopic disorder results in the appearance of first-order phase transitions between the states with different levels of atomic imbalance. The existence of a nonuniform external potential, such as trapping potential, essentially changes the lattice properties, suppressing the disorder fraction and rising the transition temperature.
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