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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, ⪡J. The critical point is found to be (J/U) ₂=0. 05974 (3), in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien Phys. Rev. B 59, 12184 (1999). 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.
Capogrosso-Sansone et al. (2008) studied this question.