Abstract
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. We find that the transition between Mott insulating phases with different fillings corresponds to first order level-crossing phase transitions. We also derive the holographic analog of the Mott/Superfluid phase transition between the homogeneous and non-homogeneous phases. We then analyze the perturbations of fields around both the Mott insulator phase and Superfluid phase.