Luttinger liquid behavior of one-dimensional 3He

TL;DR

This paper investigates the ground-state properties of one-dimensional 3He using quantum Monte Carlo methods, demonstrating Luttinger liquid behavior and identifying various physical regimes without phase transitions.

Contribution

It provides the first detailed analysis of 1D 3He, including the density dependence of the Luttinger parameter and the characterization of different physical regimes.

Findings

Luttinger liquid describes long-range correlations in 1D 3He

Density dependence of the Luttinger parameter is non-monotonic

Multiple physical regimes identified, including quasi-crystal and super-Tonks-Girardeau

Abstract

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".