  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 Mott 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.
