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

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 $r_{\text{s}}\le 1$. These are compared with the QMC results in the range of applicability of the theory.

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• Jastrow correlation factor for atoms, molecules, and solids
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• New Model System for a One-Dimensional Electron Liquid: Self-Organized Atomic Gold Chains on Ge(001)
• Ground state properties of the one-dimensional electron liquid
• Correlation effects in quasi one dimensional electron wires
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Cited by in corpus (4)

• Wire width and density dependence of the crossover in the peak of the static structure factor from $2k_{\text{F}}$ $\to$ $4k_{\text{F}}$ in one-dimensional paramagnetic electron gases
• Extended quasiparticle Padé approximation for non-Fermi liquids
• Electronic quantum wires in extended quasiparticle picture
• Off-shell selfenergy for 1-D Fermi liquids