Scale-invariant phase transition of disordered bosons in one dimension*

The disorder-induced quantum phase transition in one-dimensional bosonic systems, transitioning between superfluid and non-superfluid states, is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. However, our investigation offers a novel perspective. Here, we show that hard-core lattice bosons with integrable power-law hopping decaying with distance as 1/r^α undergo a non-BKT continuous phase transition. Employing exact quantum Monte Carlo techniques, we construct the phase diagram, with a specific focus on the α > 2 regime. We observe scale-invariant superfluid stiffness at the transition point for α ≤ 3, a characteristic incompatible with the BKT framework but typical of continuous phase transitions in higher dimensions. By scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound ν ≥ 2 and demonstrate a new universal behavior of disordered bosons in one dimension.