In this article the extended Bose-Hubbard model describing ultra-cold atomsconfined in a shallow, one-dimensional optical lattice is introduced andstudied by the exact diagonalization approach. All parameters of the model arerelated to the only relevant parameter controlled experimentally -- the depthof the optical potential. Changes in a shape of the insulating lobe in thephase diagram of the system are explored and the value of the criticaltunneling for which the system undergoes the phase transition (from theinsulating to the superfluid phase) is predicted. It is shown that the value ofcritical tunneling is substantially affected by the presence of the tunnelingsto distant sites of the optical lattice. The results may have some importancein upcoming experiments on quantum quench through phase transition points.
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