Title: Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension,
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 $\alpha$.