Susceptibility at the superfluid-insulator transition for one-dimensional disordered bosons
A pair of recent Monte Carlo studies have reported evidence for and against a crossover from weak to strong-disorder criticality in the one-dimensional dirty boson problem. The Monte Carlo analyses rely on measurement of two observables: the effective Luttinger parameter K_(eff) and the superfluid susceptibility χ. The former quantity was previously calculated analytically, using the strong-disorder renormalization group (SDRG), by Altman, Kafri, Polkovnikov, and Refael. Here, we use an extension of the SDRG framework to find a non-universal anomalous dimension η_(sd) characterizing the divergence of the susceptibility with system size: χ ~ L^(2-η_(sd)). We show that η_(sd) obeys the hyperscaling relation η_(sd) = 1/2K_(eff). We also identify an important obstacle to measuring this exponent on finite-size systems and comment on the implications for numerics and experiments.