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 a 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.

Figure 1

Possible phase diagram of a disordered 1D Bose gas as a function of the boson repulsion $U$ and disorder $\mathcal{D}$. The green dash-dotted line schematically indicates the boundary below which a bosonization description of such a problem is guaranteed (namely the disorder is smaller than the chemical potential). In this region the superfluid-Bose glass transition, denoted by the solid blue line, is described by universal exponents. The question of the nature and critical behavior of the transition in the regime for which bosonization cannot be directly applied is yet open (see text). One possibility (not shown on the figure) is that the exponent remains universal along the whole SF-BG line, leading to a single BG phase. The only singular line is then the noninteracting bosons ($U=0$) which are localized by rare events of the disorder and indicated by the blue box. The other possibility (shown in the figure), is that if at small interaction, there are nonuniversal exponents along the dashed blue line, then this forces the existence of a critical point on the SF-BG boundary between the nonuniversal and universal regime. This would imply the existence of two distinct BG phases.