We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a reentrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential. Describing these systems with a classical nonlinear sigma model and using analytical estimates supported by results from numerical simulations, we examine the nature of the ground state as a function of disorder strength, Delta, and deviation, deltanu, of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration, and in the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at small Delta and /deltanu/ to a spin glass at larger Delta or /deltanu/. We examine ground-state response functions and excitations.

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential, within the framework of a classical non-linear sigma model. We discuss the behaviour of the system using a heuristic picture for the competition between exchange and screening, and test our conclusions with extensive numerical simulations. We obtain a phase diagram for the system as a function of disorder strength and deviation of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration. In the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at weak disorder and small deviation from integer filling to a spin glass at stronger disorder or large charge deviation. We characterise the spin glass phase in terms of its magnetic and charge response, as well as its ac conductivity.Comment: 12 pages, 6 figures, REVTEX