A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasicondensate.
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.
A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HRs) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground-state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Nonanalytical contributions to the one-body density matrix are also discussed and found to be less relevant with increasing density.
The elementary excitations of one-dimensional Bose liquids interacting via a soft potential with a Lennard-Jones-type attractive tail are evaluated in the ring-diagram approximation. Starting with this potential, we have evaluated the structure factor, thermodynamic functions, pair-distribution function, ground-state energy, and sound velocity explicitly. The energy spectrum and structure factor resemble the bulk cases, but the minimum energy is much lower and the first peak of the structure factor is higher. The pair-distribution function decreases as ${r}^{\ensuremath{-}2}$ at large distances, which is characteristic of phonons in one dimension. The ground-state energy is expressed analytically in powers of a dimensionless parameter. The expression agrees with the one obtained from a $\ensuremath{\delta}$- function-type potential.
We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a3D; (iii) enters a unitary regime for |a3D| → ∞, where the properties of the gas are independent of a3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.
The zero-temperature dynamical structure factor $S(q,\ensuremath{\omega})$ of one-dimensional hard rods is computed using state-of-the-art quantum Monte Carlo and analytic continuation techniques, complemented by a Bethe ansatz analysis. As the density increases, $S(q,\ensuremath{\omega})$ reveals a crossover from the Tonks-Girardeau gas to a quasisolid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\ensuremath{\omega})$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\ensuremath{\omega})$ at specific wave vectors ${\mathcal{Q}}_{n}=n2\ensuremath{\pi}/a$, where
a is the core radius, resulting from the interplay of the particle-hole boundaries of suitably rescaled ideal Fermi gases. We observe significant similarities between hard rods and one-dimensional
4He at high density, suggesting that the hard-rods model may provide an accurate description of dense one-dimensional liquids of quantum particles interacting through a strongly repulsive, finite-range potential.