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

TL;DR

This work investigates how finite transverse confinement in quasi-one-dimensional paramagnetic electron wires affects correlation-driven ordering. Using variational quantum Monte Carlo with Slater-Jastrow-backflow wavefunctions, it analyzes ground-state properties across wire widths $b$ and density parameters $r_ ext{s}$, focusing on the crossover in the static structure factor from $k=2k_ ext{F}$ to $k=4k_ ext{F}$ in the charge sector and the associated spin behavior. The results show that decreasing $b$ at fixed $r_ ext{s}$ promotes a $2k_ ext{F} ightarrow4k_ ext{F}$ crossover—consistent with a finite-width induced quasi-Wigner crystal—with complete spin-charge decoupling evidenced by distinct peaks in charge and spin structure factors; the charge and spin peak heights follow finite-width theory fits and bosonization-inspired forms, and the Tomonaga-Luttinger parameter $K_ ho$ is strongly sensitive to $b$ and $r_ ext{s}$. These findings illuminate how confinement controls ordering tendencies and spin-charge separation in 1D electron fluids, with implications for designing nanoscale quasi-1D electronic systems.

Abstract

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 $K_ρ$ is found to be significant.

Figures (7)

• Figure 1: Correlation energy per particle ($E_\text{c}$) as a function of wire width $b$ for $r_\text{s}$ = 0.5, 1, and 2 (top to bottom).
• Figure 2: Charge structure factor $S_{\rho\rho}(k)$ plotted against $k/k_\text{F}$ (a)--(c) and charge-charge pair correlation function plotted against $r/r_\text{s}$ (d)--(f) for $r_\text{s}=0.5$, 2, and 5 for various $b$ values with $N=98$ electrons. The insets in (b) and (c) show the peak at $k=4k_\text{F}$ in greater detail.
• Figure 3: Spin structure factor $S_{\sigma\sigma}(k)$ plotted against $k/k_\text{F}$ (a)--(c) and spin-spin pair correlation function plotted against $r/r_\text{s}$ (d)--(f) for $r_\text{s}=0.5$, 1, and 2 for various $b$ values with $N=98$ electrons. The insets (a), (b), and (c) show the peak at $k=2k_\text{F}$ in greater detail.
• Figure 4: (Top) Charge SSF peak height at $k= 4k_\text{F}$ as a function of wire width $b$ for $r_\text{s}=0.5$, 1, and 2 for $N=98$ electrons. The peak heights at $k=4k_\text{F}$ are fitted by Eq. (\ref{['Eq:cSSF4kf_fit']}) and the fits are shown by solid lines, whereas the $2k_\text{F}$ peak heights are joined by dashed lines. (Bottom) Height of spin SSF plotted against $b$ for $r_\text{s}=0.5$, 1, and 2 for $N=98$ electrons and fitted by Eq. (\ref{['Eq:sSSF2kf_fit']}).
• Figure 5: MD against $k/k_\text{F}$ for different values of wire width $b$ and $r_\text{s}$ for $N=98$ electrons.