Numerical evidence for strong randomness scaling at a superfluid-insulator transition of one-dimensional bosons

TL;DR

This paper provides numerical Monte Carlo evidence that the superfluid-insulator transition in disordered one-dimensional bosons is governed by a strong-randomness critical point, characterized by universal weak link distributions and non-universal Luttinger parameters.

Contribution

It offers the first numerical verification of the strong-randomness critical point controlling the transition, aligning Monte Carlo results with strong disorder renormalization group predictions.

Findings

Distribution of superfluid stiffness shows a power-law tail.

Luttinger parameter is non-universal at the critical point.

Good agreement with theoretical scaling predictions.

Abstract

We present numerical evidence from Monte Carlo simulations that the superfluid-insulator quantum phase transition of interacting bosons subject to strong disorder in one dimension is controlled by the strong-randomness critical point. At this critical point the distribution of superfluid stiffness over disorder realizations develops a power-law tail reflecting a universal distribution of weak links. The Luttinger parameter on the other hand does not take on a universal value at this critical point, in marked contrast to the known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in weakly disordered systems. We develop a finite-size scaling procedure which allows us to directly compare the numerical results from systems of linear size up to 1024 sites with theoretical predictions obtained by Altman et al. [ Phys. Rev. Lett. 93 150402 (2004)] using a strong disorder renormalization group approach. The data shows good agreement with the scaling expected at the strong-randomness critical point.