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

TL;DR

This paper investigates the effects of electron correlation and confinement in high-density quasi-one-dimensional quantum wires using quantum Monte Carlo and RPA methods, revealing how wire width influences correlation energy and Tomonaga-Luttinger liquid parameters.

Contribution

It provides new quantitative analysis of correlation effects in quantum wires at high density, combining QMC simulations with analytical RPA expressions for different confinement models.

Findings

Static structure factor peak grows as wire width decreases.

Tomonaga-Luttinger parameter $K_\rho$ increases with wire width.

Correlation energy varies as $b^2$ for small wire widths.

Abstract

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 $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ 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 $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ 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 $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.