# Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension

## TL;DR

This study uses advanced simulations to analyze the superfluid to Bose glass transition in one-dimensional attractive hard-core bosons, revealing a critical line with two regimes distinguished by interaction strength and disorder effects.

## Contribution

It identifies a Berezinskii-Kosterlitz-Thouless critical line with universal and non-universal regimes, highlighting the role of weak links and power-law distributions in the transition.

## Key findings

- Universal critical Luttinger parameter $K_c=3/2$ at weak attraction.
- Non-universal $K_c>3/2$ at stronger attraction with weak-link physics.
- Power-law distributed weak links with a variable exponent $eta$ in strong disorder regime.

## Abstract

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent $\alpha$.