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 chi. 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 nonuniversal anomalous dimension eta(sd) characterizing the divergence of the susceptibility with system size, chi similar to L2-eta sd. We show that eta(sd) obeys the hyperscaling relation eta(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.