Abstract
We study long-range orders in one-dimensional Bose-Hubbard model with power-law long-range hoppings. We measure the correlation and the winding numbers of hardcore bosons in one-dimension ring using quantum Monte Carlo simulations to calculate the condensate fraction and the superfluid density. On the other hand, we calculate the Entanglement entropy of open boundary zero-temperature ground states via density matrix renormalization group to estimate the central charge of the system.