Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions

We investigate the superfluid (SF) to Bose glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. $T=0$ critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder $W_c=4.80(5)$. Our results give the following estimates for the critical exponents: $z=1.85(15)$, $\nu =1.20(12)$, $\eta =-0.40(15)$. Furthermore, the probability distribution of the SF response $P(\ln {\rho }_{\mathrm{s}\mathrm{f}})$ displays striking differences across the transition: while it narrows with increasing system sizes $L$ in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point $P(\ln {\rho }_{\mathrm{s}\mathrm{f}}+z\ln L)$ is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.