Scale-invariant phase transition of disordered bosons in one dimension

The disorder-induced quantum phase transition between superfluid and non-superfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with integrable power-law hopping decaying with distance as $1\mathrm{/}{r}^{\alpha }$ - corresponding in spin language to a $XY$ model with power-law couplings - undergo a non-BKT continuous phase transition instead. We use exact quantum Monte-Carlo methods to determine the phase diagram for different values of the exponent $\alpha$, focusing on the regime $\alpha >2$. We find that the scaling of the superfluid stiffness with the system size is scale-invariant at the transition point for any $\alpha \le 3$ - a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\nu \ge 2$ and demonstrate a new universal behavior of disordered bosons in one dimension. For $\alpha >3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.