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 study uses variational quantum Monte Carlo to analyze how wire width and electron density influence the crossover in the static structure factor from $2k_F$ to $4k_F$ in one-dimensional paramagnetic electron gases, revealing the interplay of these parameters.

Contribution

It introduces a detailed analysis of the effects of wire width and electron density on the static structure factor crossover using VMC, with theoretical fits based on finite wire width theory and bosonization.

Findings

Crossover from $2k_F$ to $4k_F$ peaks occurs as wire width decreases at fixed density.

Finite wire width significantly affects charge and spin structure factors and correlation energy.

Charge and spin degrees of freedom are fully decoupled at the peaks.

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 $K_{\rho}$ is found to be significant.