We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^{\alpha }$ using exact large scale quantum Monte Carlo simulations. For all $1<\alpha \le 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for $\alpha >3$. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime $1<\alpha \le 3$. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for $\alpha \le 2$, anomalous quasi-long-range order for $2<\alpha \le 3$, and conventional algebraic decay for $\alpha >3$. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.

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• Bosons
• Cold gases in optical lattices
• Long-range interactions
• Quantum phase transitions
• Quantum spin models
• Trapped ions
• Ultracold gases
• Bose-Hubbard model
• Quantum Monte Carlo
• XY model