Dynamics and thermodynamics of the Bose-Hubbard model

We report results from a systematic analytic strong-coupling expansion of t he Bose-Hubbard model in one- and two-spatial dimensions. We obtain numeric ally exact results for the dispersion of single-particle and single-hole ex citations in the Mott insulator. The boundary of the Mott phase can be dete rmined with previously unattainable accuracy in one and two dimensions. In one dimension, we observe the occurrence of reentrant behavior from the com pressible to the insulating phase in a region close to the critical point, which was conjectured in earlier work. Our calculation can be used as a ben chmark for the development of numerical techniques for strongly correlated systems. [S0163-1829(99)04319-2].