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Correlation effects in one-dimensional metallic quantum wires under various confinements

Vidit Gangwar1, Vinod Ashokan1,*, Ankush Girdhar2, Klaus Morawetz3,4, N. D. Drummond5, and K. N. Pathak6

  • *Contact author: ashokanv@nitj.ac.in
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Phys. Rev. B 112, 245426 – Published 23 December, 2025

DOI: https://doi.org/10.1103/zqcj-f5f6

Abstract

Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths b and density parameters rs. In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of b and rs. Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire (b→0) in the high-density limit, we find that the correlation energy for transverse confinement models V1(q) (harmonic), V2(q) (cylindrical), and V5(q) (harmonic-delta) approaches εc(rs)=−π2/360∼−0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, J. Chem. Phys. 138, 064108 (2013); V. Ashokan, et al., Phys. Rev. B 101, 075130 (2020)]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance x=0 to yield the same correlation energy. In contrast, other confinement potentials, V3(q) (infinite square well), V4(q) (infinite square-infinite triangular well), and V6(q) (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to εc∼−0.03002 a.u. for these potentials. The percentage difference in correlation energy between the confinement models V1(q), V2(q), V5(q) and V3(q), V4(q), V6(q) is within about 10% in the high-density limit. The ground-state properties obtained from the FRPA are compared with the available quantum Monte Carlo results in the high-density regime. We observe that the peak height in the static structure factor at k=2kF depends significantly on the confinement model. These prominent peaks at k=2kF are fitted with a function based on our finite wire-width theory, guided by insights from bosonization, demonstrating good agreement with our FRPA theory.

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Phys. Rev. B 112, 245426– Published 23 December, 2025
  • Received 17 July 2025
  • Revised 26 November 2025
  • Accepted 9 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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