  We present numerical evidence from Monte Carlo simulations that the
superfluid-insulator quantum phase transition of interacting bosons subject to
strong disorder in one dimension is controlled by the strong-randomness
critical point. At this critical point the distribution of superfluid stiffness
over disorder realizations develops a power-law tail reflecting a universal
distribution of weak links. The Luttinger parameter on the other hand does not
take on a universal value at this critical point, in marked contrast to the
known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in
weakly disordered systems. We develop a finite-size scaling procedure which
allows us to directly compare the numerical results from systems of linear size
up to 1024 sites with theoretical predictions obtained by Altman et al. [ Phys.
Rev. Lett. 93 150402 (2004)] using a strong disorder renormalization group
approach. The data shows good agreement with the scaling expected at the
strong-randomness critical point.
