We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors applies for both classical Berezinskii-Kosterlitz-Thouless transition at a finite temperature and quantum phase transition from superfluid to

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... t insulator. Our results show that the critical regime can be as large as a few lattice sites in optical lattice and should be observable in present experimental conditions.