Possibility of direct Mott insulator-to-superfluid transitions in weakly disordered boson systems

We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent $\nu .$ In the presence of weak disorder, we obtain $\nu =0.5\mathrm{}\pm 0.1,$ the same value as that in the pure model, near the tip of a Mott insulator lobe, using the dynamical critical exponent $z=2.\mathrm{}$ As the strength of disorder is increased beyond a certain value, however, the value of $\nu$ is found to change to $0.9\pm \mathrm{0.1.}$ This result strongly suggests that there exist direct Mott insulator-to-superfluid transitions around the tip of a Mott insulator lobe in the weak disorder regime.