Luttinger liquid behavior of one-dimensional 3He

The ground-state properties of one-dimensional 3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well reproduced by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation function. The density dependence of the Luttinger parameter is explicitly found and interestingly it shows a non-monotonic 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 "quasi-crystal".