Wire width and density dependence of the crossover in the peak of the static structure factor from 2kF2k_\text{F} →\rightarrow 4kF4k_\text{F} in one-dimensional paramagnetic electron gases

We use the variational quantum Monte Carlo (VMC) method to study the wire width ($b$) and electron density ($r_\text{s}$) dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density, and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2k_\text{F}$ to $k=4k_\text{F}$. It is found that for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2k_\text{F}$ to $4k_\text{F}$ occurs as the wire width decreases. Our study suggests that the crossover is due to interplay of both $r_\text{s}$ and $b<r_\text{s}$. The finite wire width correlation effect is reflected in the peak height of the charge and spin structure factors. We fit the dominant peaks of the charge and spin structure factors assuming fit functions based on our finite wire width theory and clues from bosonization, resulting in a good fit of the VMC data. The pronounced peaks in the charge and spin structure factors at $4 k_\text{F}$ and $2 k_\text{F}$, respectively, indicate the complete decoupling of the charge and spin degrees of freedom. Furthermore, the wire width dependence of the electron correlation energy and the Tomonaga-Luttinger parameter $K_{\rho}$ is found to be significant

Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths b and density parameters r s . The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at k = 2 k F grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter K ρ from the momentum density. It is found that K ρ increases by about 10% between wire widths b = 0.01 and b = 0.5 . We also obtain ground-state properties of finite-thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for b ≪ r s < 1 . It is found that the correlation energy varies as b 2 for b ≪ r s from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of b and r s ≤ 1 . These are compared with the QMC results in the range of applicability of the theory

Wigner crystallization in quasi-one-dimensional quantum wire

Abstract We study the ground-state properties of quasi-one-dimensional paramagnetic electron fluid using variational quantum Monte Carlo method. The electrons are transversally confined using the harmonically regularized Coulomb potential with long range order. In this work we have investigated the crossover from liquid to crystalline phase in the finite width paramagnetic quantum wire. The calculated pair correlation function shows the oscillations of period $$2r_\text {s} a_0$$ 2 r s a 0 , where $$a_0$$ a 0 is the Bohr’s radius and $$r_\text {s}$$ r s is Wigner Seitz radius or electron-density parameter which corresponds to a $$k=4k_\text {F}$$ k = 4 k F peak with $$k_\text {F}$$ k F being Fermi wave vector in the static structure factor at finite electron density. It is a signature of the onset of Wigner crystallization. It is found that the cross-over from liquid to a quasi-Wigner phase is due to enhancement of the electron correlation effects as $$r_\text {s}$$ r s increases or as the wire width b decreases