  We present a holographic construction of the large-N Bose-Hubbard model. The
model is based on Maxwell fields coupled to charged scalar fields on the AdS2
hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model
and find that the model admits Mott insulator ground states in the limit of
large Coulomb repulsion. In the Mott insulator phases, the bosons are localized
on each site. At zero hopping we find that the transitions between Mott
insulating phases with different fillings correspond to first order
level-crossing phase transitions. At finite hopping we find a holographic phase
transition between the Mott phase and a non-homogeneous phase. We then analyze
the perturbations of fields around both the Mott insulator phase and
inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.
