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