Bose-Hubbard model with power-law hopping in one dimension

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^α$ using exact large scale Quantum Monte-Carlo simulations. For all $1<α\leq 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in a way incompatible with the Berezinskii-Kosterlitz-Thouless (BKT) scenario, which is recovered for $α>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $α$ and from careful analysis of the spectrum. Large-scale simulations of the grand canonical phase diagram and of the decay of correlation functions demonstrate an overall behavior akin to higher dimensional systems with long-range order in the ground state for $α\leq 2$ and intermediate between one and higher dimensions for $2<α\leq 3$. 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.