Susceptibility at the superfluid-insulator transition for one-dimensional disordered bosons

Abstract

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 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. © 2013 American Physical Society.