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 Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, momentum are calculated at high density, $r_\text{s}=0.5$. It is observed that peak in factor $k=2k_\text{F}$ grows as width decreases. obtain Tomonaga-Luttinger liquid parameter $K_\rho$ from density. found increases by about $10$\% between $b=0.01$ $b=0.5$. also finite thickness theoretically first-order random phase approximation (RPA) with exchange self-energy contributions, which exact high-density limit. Analytical expressions energy derived $b \ll r_\text{s}<1$. varies $b^2$ r_\text{s}$ its value an infinitely thin wire. depends significantly on model used (harmonic versus cylindrical confinement). RPA numerically evaluated several values $r_\text{s} \leq 1$. These compared QMC results range applicability theory.