Quantum Critical Behavior of the Superfluid-Mott Glass Transition

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical (2+1)-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents z=1.52(3), ν =1.16(5), ß/ν =0.48(2), γ/ν=2.52(4), and η = -0.52(4). These values agree with and improve upon earlier Monte Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments