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Using a strong disorder real-space renormalization group (RG), we study thephase diagram of a fully disordered chain of interacting bosons. Since thisapproach does not suffer from run-away flows, it allows a direct study of theinsulating phases, which are not accessible in a weak disorder perturbativetreatment. We find that the universal properties of the insulating phase aredetermined by the details and symmetries of the onsite chemical-potentialdisorder. Three insulating phases are possible: (i) an incompressible Mottglass with a finite superfluid susceptibility, (ii) a random-singlet glass withdiverging compressibility and superfluid susceptibility, (iii) a Bose glasswith a finite compressibility but diverging superfluid susceptibility. Inaddition to characterizing the insulating phases, we show that thesuperfluid-insulator transition is always of the Kosterlitz-Thoulessuniversality class.

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