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 weakto strongdisorder criticality in the one-dimensional dirty boson problem. The Monte Carlo analyses rely on measurement of two observables: the effective Luttinger parameter Keff 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 nonuniversal anomalous dimension ηsd characterizing the divergence of the susceptibility with system size, χ ∼ L2−ηsd . We show that ηsd obeys the hyperscaling relation ηsd = 1/2Keff . We also identify an important obstacle to measuring this exponent on finite-size systems and comment on the implications for numerics and experiments.