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.
A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at
T=0, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.
We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around
kF, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.
We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$, the one-body density matrix
n(x), the pair distribution function
g(x), and the static structure factor
S(q) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter
K. The 1D Bose fluid examined is a single chain of
4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid
4He. In this range,
K varies from
K>2 at low density, where a robust superfluid is predicted, to
K<0.5, where fragile 1D superflow and solidlike peaks in
S(q) are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The
n(x) and
g(x) show long range oscillations and decay with
x as predicted by LL theory. The amplitude of the oscillations is large at high density (small
K) and small at low density (large
K). The
K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single
vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.
Structural and dynamic correlations in the ground state of the one-dimensional Fermi one-component plasma are studied by Quantum Monte Carlo simulations. Results are presented for the pair correlation function, static structure factor, the one-particle density matrix and the momentum distribution, for the cases of full, partial and no polarization. {Within the precision of the calculation, the results conform to the fundamental scaling prediction of the Tomonaga-Luttinger Liquid Theory}. Evidence is reported of density correlations slowly decaying with distance, with the concurrent emergence of quasi-crystalline order even in the weakly correlated regime. Effects of quantum statistics in the momentum distribution are discussed.