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The Bose-Hubbard model exhibits a rich phase diagram consisting both ofinsulating regimes where diagonal long range (solid) order dominates as well asconducting regimes where off diagonal long range order (superfluidity) ispresent. In this paper we describe the results of Quantum Monte Carlocalculations of the phase diagram, both for the hard and soft core cases, witha particular focus on the possibility of simultaneous superfluid and solidorder. We also discuss the appearance of phase separation in the model. Thesimulations are compared with analytic calculations of the phase diagram andspin wave dispersion.Comment: 28 pages plus 24 figures, uuencoded Revtex+postscript file

Simultaneous diagonal and off-diagonal order in the Bose-Hubbard Hamiltonian