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One Dimensional 1H, 2H and 3H

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.