  We employ large-scale Monte Carlo simulations to study a particle-hole
symmetric site-diluted quantum rotor model in two dimensions. The ground state
phase diagram of this system features two distinct quantum phase transitions
between the superfluid and the insulating (Mott glass) phases. They are
separated by a multicritical point. The generic transition for dilutions below
the lattice percolation threshold is driven by quantum fluctuations while the
transition across the percolation threshold is due to the geometric
fluctuations of the lattice. We determine the location of the multicritical
point between these two transitions and find its critical behavior. The
multicritical exponents read $z=1.72(2)$, $\beta/\nu=0.41(2)$, and
$\gamma/\nu=2.90(5)$ . We compare our results to other quantum phase
transitions in disordered systems, and we discuss experiments.
