The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.

• Received 10 December 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.050403