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The role of collective phonon excitations on the properties of cold atoms inoptical lattices is investigated. These phonon excitations are collectiveexcitations, whose appearance is caused by intersite atomic interactionscorrelating the atoms, and they do not arise without such interactions. Thesecollective excitations should not be confused with lattice vibrations producedby an external force. No such a force is assumed. But the considered phononsare purely self-organized collective excitations, characterizing atomicoscillations around lattice sites, due to intersite atomic interactions. It isshown that these excitations can essentially influence the possibility of atomsto be localized. The states that would be insulating in the absence of phononexcitations can become delocalized when these excitations are taken intoaccount. This concerns long-range as well as local atomic interactions. Tocharacterize the region of stability, the Lindemann criterion is used.

Instability of insulating states in optical lattices due to collective phonon excitations