The disorder-induced quantum phase transition between superfluid and nonsuperfluid 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 power-law hopping decaying with distance as $1/r^{\alpha }$ with a finite integral over space—corresponding in spin language to an $XY$ 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 a 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 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.

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• Cold gases in optical lattices
• Hard-core bosons
• Long-range interactions
• Quantum phase transitions
• XY model
• Disordered systems
• Quantum spin models
• Ultracold gases
• Quantum Monte Carlo