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

Gangwar, Vidit and Ashokan, Vinod and Girdhar, Ankush and Morawetz, Klaus and Drummond, Neil and Pathak, K. N. (2025) Correlation effects in one-dimensional metallic quantum wires under various confinements. Physical Review B, 112 (24): 245426. ISSN 2469-9950

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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 $r_\text{s}$. 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 $r_\text{s}$. Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire $(b\rightarrow 0)$ in the high-density limit, we find that the correlation energy for transverse confinement models $V_1(q)$ (harmonic), $V_2(q)$ (cylindrical), and $V_5(q)$ (harmonic-delta) approaches $\epsilon_\text{c}(r_\text{s})= - \pi^2/360 \sim -0.02741$ a.u., which agrees with the exact results in this limit [P.-F.\ Loos, J.\ Chem.\ Phys.\ \textbf{138}, 064108 (2013), V.\ Ashokan \textit{et al.}, Phys.\ Rev.\ B \textbf{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, $V_3(q)$ (infinite square well), $V_4(q)$ (infinite square-infinite triangular well), and $V_6(q)$ (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to $\epsilon_\text{c} \sim -0.03002$ a.u.\ for these potentials. The percentage difference in correlation energy between the confinement models $V_1(q)$, $V_2(q)$, $V_5(q)$ and $V_3(q)$, $V_4(q)$, $V_6(q)$ 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 $k=2k_\text{F}$ depends significantly on the confinement model. These prominent peaks at $k=2k_\text{F}$ are fitted with a function based on our finite wire-width theory, guided by insights from bosonization, demonstrating good agreement with our FRPA theory.