Separation of two regimes in a disordered boson Hubbard Model

We study the insulator-to-superfluid transition in a two-dimensional disordered boson Hubbard model at zero temperature for intermediate strength of disorder at commensurate density. Via Monte Carlo calculations of the correlation functions in the integer current representation of the model, we obtain the dynamical critical exponent $z=1.5 \pm 0.1$, supporting the multi-critical behavior separating the strong and weak disorder regimes. Investigating the density profile, we suggest that the density fluctuations due to the particle-hole excitations drive the transition in the weak disorder regime.