Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La$_{2}$Cu$_{1-p}$(Zn,Mg)$_{p}$O$_{4}$. Our results are also relevant for disordered interacting boson systems.