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We study the quantum phase transition between the superfluid and the Mottinsulator in the one-dimensional (1D) Bose-Hubbard model. Using thetime-evolving block decimation method, we numerically calculate the tunnelingsplitting of two macroscopically distinct states with different windingnumbers. From the scaling of the tunneling splitting with respect to the systemsize, we determine the critical point of the superfluid to Mott insulatortransition for arbitrary integer filling factors. We find that the criticalvalues versus the filling factor in 1D, 2D, and 3D are well approximated by asimple analytical function. We also discuss the condition for determining thetransition point from a perspective of the instanton method.

Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors