Susceptibility at the Superfluid-Insulator Transition for One-Dimensional Disordered Bosons

TL;DR

This paper extends the strong-disorder renormalization group framework to analyze the superfluid-insulator transition in one-dimensional disordered bosons, revealing a non-universal anomalous dimension that influences susceptibility divergence.

Contribution

It introduces an extended SDRG approach to determine the anomalous dimension eta_{sd} and its relation to the effective Luttinger parameter, clarifying measurement challenges.

Findings

Derived the relation eta_{sd} = 1/2K_{eff}

Identified obstacles in finite-size system measurements

Provided insights for numerical and experimental studies

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.