  One of the most promising applications of ultracold gases in optical lattices
is the possibility to use them as quantum emulators of more complex condensed
matter systems. We provide benchmark calculations, based on exact quantum Monte
Carlo simulations, for the emulator to be tested against. We report results for
the ground state phase diagram of the two-dimensional Bose-Hubbard model at
unity filling factor. We precisely trace out the critical behavior of the
system and resolve the region of small insulating gaps, \Delta << J. The
critical point is found to be (J/U)_c=0.05974(3), in perfect agreement with the
high-order strong-coupling expansion method of Ref. 1. In addition, we present
data for the effective mass of particle and hole excitations inside the
insulating phase and obtain the critical temperature for the superfluid-normal
transition at unity filling factor.
