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We show that the critical point of the two-dimensional Bose-Hubbard model canbe easily found through studies of either on-site atom number fluctuations orthe nearest-neighbor two-point correlation function (the expectation value ofthe tunnelling operator). Our strategy to locate the critical point is based onthe observation that the derivatives of these observables with respect to theparameter that drives the superfluid-Mott insulator transition are singular atthe critical point in the thermodynamic limit. Performing the quantum MonteCarlo simulations of the two-dimensional Bose-Hubbard model, we show that thistechnique leads to the accurate determination of the position of its criticalpoint. Our results can be easily extended to the three-dimensional Bose-Hubbardmodel and different Hubbard-like models. They provide a simpleexperimentally-relevant way of locating critical points in various cold atomiclattice systems.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables