PHASE-DIAGRAM OF THE BOSE-HUBBARD MODEL

The first reliable analytic calculation of the phase diagram of the Bo se gas on a d-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the devi ations from the Monte Carlo calculations are larger, but the correct s hape of the Mott-insulator lobes is still obtained. Explicit expressio ns for the energy of the Mott and the <<defect>> phase are given in a strong-coupling expansion.