The insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group (RG), we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from run-away flows, it allows a direct study of the insulating phases, which are not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the onsite chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always of the Kosterlitz-Thouless universality class.