Anomalous quantum glass of bosons in a random potential in two dimensions

We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.