# Luttinger parameter of quasi-one-dimensional para-H2

## TL;DR

This study uses Monte Carlo simulations to analyze how the Luttinger parameter of para-hydrogen varies with density in one-dimensional and quasi-one-dimensional setups, revealing it remains in the quasi-crystal regime.

## Contribution

It provides the first detailed analysis of the Luttinger parameter dependence on density in quasi-one-dimensional para-hydrogen using exact ground-state Monte Carlo methods.

## Key findings

- Luttinger parameter increases with density in quasi-one-dimensional para-H2.
- System remains in the quasi-crystal regime, not reaching superfluidity.
- Quasi-one-dimensional confinement influences the Luttinger parameter but does not induce superfluid behavior.

## Abstract

We have studied the ground-state properties of para-hydrogen in one dimension and in quasi-one-dimensional configurations using the path integral ground state Monte Carlo method. This method produces zero-temperature exact results for a given interaction and geometry. The quasi-one-dimensional setup has been implemented in two forms: the inner channel inside a carbon nanotube coated with H$_2$ and a harmonic confinement of variable strength. Our main result is the dependence of the Luttinger parameter on the density within the stable regime. Going from one dimension to quasi-one dimension, keeping the linear density constant, produces a systematic increase of the Luttinger parameter. This increase is however not enough to reach the superfluid regime and the system always remain in the quasi-crystal regime, according to Luttinger liquid theory.