One Dimensional 1H, 2H and 3H

TL;DR

This paper investigates the ground-state properties of one-dimensional hydrogen isotopes using quantum Monte Carlo methods, revealing how isotope mass influences various physical regimes and behaviors in these quantum systems.

Contribution

It provides detailed equations of state, correlation functions, and structure factors for hydrogen isotopes, and interprets them within Luttinger liquid theory, highlighting isotope-dependent physical regimes.

Findings

Identification of different physical regimes for isotopes

Density dependence of the Luttinger parameter

Rich behavior observed in tritium isotope

Abstract

The ground-state properties of one-dimensional electron-spin-polarized hydrogen $^1$H, deuterium $^2$H, and tritium $^3$H are obtained by means of quantum Monte Carlo methods. The equations of state of the three isotopes are calculated for a wide range of linear densities. The pair correlation function and the static structure factor are obtained and interpreted within the framework of the Luttinger liquid theory. We report the density dependence of the Luttinger parameter and use it to identify different physical regimes: Bogoliubov Bose gas, super-Tonks-Girardeau gas, and quasi-crystal regimes for bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for fermions. We find that the tritium isotope is the one with the richest behaviour. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.