Superfluidity of interacting bosons in one-dimension via strong disorder

We have found a novel set of superfluid and Mott insulating phases arising in strongly-disordered, one-dimensional optical lattices with large, commensurate filling of bosons. Using a spin-wave approach, we show that the bosons form a true, long-range ordered superfluid at $T=0$, provided that the on-site repulsion has a broad distribution. Such broad, power-law distributions arise naturally under real-space renormalization group flow. Furthermore, they describe the asymptotic properties of diluted two-dimensional optical lattices near percolation threshold. We discuss the possibility of true superfluidity in the diluted system.