Weak- versus strong-disorder superfluid-Bose glass transition in one dimension

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 nonuniversal 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.