  The ground state and structure of a one-dimensional Bose gas with dipolar
repulsions is investigated at zero temperature by a combined Reptation Quantum
Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid
behavior emerges in a wide range of intermediate densities, evolving into a
Tonks-Girardeau gas at low density and into a classical quasi-ordered state at
high density. The density dependence of the Luttinger exponent is extracted
from the numerical data, providing analytical predictions for observable
quantities, such as the structure factor and the momentum distribution. We
discuss the accessibility of such predictions in current experiments with
ultracold atomic and molecular gases.
