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 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 non-universal anomalous dimension eta_{sd} characterizing the divergence of the susceptibility with system size: chi ~ L^(2-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.

4.5 pages, 3 figures

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Cited by in corpus (3)

• Strong Disorder RG approach - a short review of recent developments
• Numerical evidence for strong randomness scaling at a superfluid-insulator transition of one-dimensional bosons
• Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the Sine-Gordon transition: a Worm Algorithm Monte Carlo study