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

Girdhar, Ankush and Ashokan, Vinod and Drummond, Neil and Morawetz, Klaus and Pathak, K. N. (2022) Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density. Physical Review B: Condensed Matter and Materials Physics, 105 (11). ISSN 1098-0121

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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 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 = 2 k F grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter K ρ from the momentum density. It is found that K ρ 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.