One dimensional¹H,²H and³H

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 behavior. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.

Few-body route to one-dimensional quantum liquids

“…The results are shown in Figs. 2 and 3, and are in excellent agreement with the Monte Carlo results of references [9][10][11]. As noted above, the universality hypothesis at the two-body level implies K L = 1 whenever θ(k F ) = 0 which, as seen in Figs.…”

“…Essentially, many correlation functions, and the excitation spectrum, have universal behaviours, and the non-universal parameters -the Luttinger parameter and speed of soundare the only system-dependent quantities of interest. To extract these, however, one needs to either invoke perturbation theory, only valid for weak interactions, or to solve the many-body problem numerically "exact" using Monte Carlo [6,[9][10][11] for continuous or DMRG methods [12] for lattice models, or quasi-analytically for integrable models via the Bethe ansatz [8,13]. In this Letter, we develop a simple, yet highly non-perturbative method, that uses only two-body scattering information to extract the speed of sound and Luttinger parameter of strongly interacting many-body quantum systems in one dimension.…”

“…In this Letter, we develop a simple, yet highly non-perturbative method, that uses only two-body scattering information to extract the speed of sound and Luttinger parameter of strongly interacting many-body quantum systems in one dimension. To show the reliability of our theory, we study all the stable isotopes of helium and spin-polarised hydrogen, and tritium, when tightly confined to one dimension, using realistic molecular potentials, which are stronglyinteracting and intractable with perturbative methods, and compare our results to the Monte Carlo data of references [9][10][11]. Using similar methods, we also study the liquid phase of 4 He, which is not a Luttinger liquid.…”

“…There, we observe that the results are highly non-perturbative and are valid beyond the perturbative regime and down to γ ≈ 5, and that our results interpolate between the Bogoliubov and the Tonks-Girardeau regimes. [10] and [11].…”

Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials

“…Since, according to the LL theory, a system's response in the low-energy limit should depend on the parameter K, we choose a model in which, depending on the density, K assumes values from ∞ to 0. Such behavior in one dimension is demonstrated by the 4 He atoms [16] or isotopes of spin-polarized hydrogen [29]. This allows us to study the regime where superfluidity is expected to be robust (K > 2) and the other one where even an infinitesimal periodic potential is expected to destroy superfluidity [2].…”