SCALING LAW OF SUPERFLUID–INSULATOR TRANSITION IN THE 1D BOSE–HUBBARD MODEL

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.