A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at $T=0$, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.

• Received 21 November 2006

DOI:https://doi.org/10.1103/PhysRevA.75.051602