Luttinger-liquid behavior of one-dimensional 3He

The ground-state properties of one-dimensional He-3 are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a "Bose gas." a "super-Tonks-Girardeau" regime, and a "quasicrystal." The obtained results are applicable to unpolarized, partially, or fully polarized He-3.