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 = 2k(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. 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.

Automated summary

The ground-state properties of ferromagnetic quasi-one-dimensional quantum wires at high density were studied using the quantum Monte Carlo method. It was observed that the peak in the static structure factor grows as the wire width decreases. The Tomonaga-Luttinger liquid parameter K-rho was obtained from the momentum density, with an increase of about 10% between different wire widths. The first-order random phase approximation (RPA) was used to examine the ground-state properties of finite-thickness wires, showing variations in correlation energy depending on the wire model. Comparisons were made with numerical evaluations for several values of wire widths and density parameters.