Phase transition of interacting disordered bosons in one dimension

Interacting bosons generically form a superfluid state. In the presence of disorder it can get converted into a compressible Bose glass state. Here we study such transition in one dimension at moderate interaction using bosonization and renormalization group techniques. We derive the two-loop scaling equations and discuss the phase diagram. We find that the correlation functions at the transition are characterized by universal exponents in a finite region around the fixed point.