10-12E

Appearance of the Bose-Einstein condensate (BEC) in the lattice Bose gas is investigated for the case of particle quantum hopping between the local excited states. The present study is performed on the basis of the Bose-Hubbard model (widely used in the theory of optical lattices with ultracold atoms and ionic conductors as well as for description of quantum delocalization of adsorbed particles) in the hard-core boson limit. It has been proved that the order of the phase transition can change from the second to the first one depending on values of the excitation energy, the particle chemical potential and temperature. Conditions of the phase separation into normal and BEC phases have been also established.