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

TL;DR

This study investigates how different transverse confinement models affect electron correlations in one-dimensional quantum wires using the FRPA method, revealing model-dependent variations in correlation energy and structure factors.

Contribution

It provides a detailed comparison of correlation energies and ground-state properties across various confinement potentials in 1D quantum wires using an advanced theoretical approach.

Findings

Correlation energy approaches a universal limit for some models in high-density limit.

Different confinement models yield significantly different static structure factors.

FRPA results agree well with quantum Monte Carlo simulations.

Abstract

Dynamical response theory is used to investigate 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 $r_{\rm s}$. Using the first-order random phase approximation (FRPA), which provides the ground state structure beyond the random phase approximation, we compute the structure factor, pair-correlation function, correlation energy, and ground-state energy. The correlation energy depends on the choice of confinement model and hence effective electron-electron interaction. For the ultrathin wire ($b\rightarrow 0$) in the high-density limit, the correlation energy for transverse confinement models $V_1(q)$ (harmonic), $V_2(q)$ (cylindrical), and $V_5(q)$ (harmonic-delta) approaches $\epsilon_{\rm c}(r_{\rm s})= - \pi^2/360 \sim -0.02741$ a.u., which agrees with the exact results in this limit [J. Chem. Phys. 138, 064108 (2013); Phys. Rev. B 101, 075130 (2020)]. 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, $V_3(q)$ (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 $\epsilon_{\rm c} \sim -0.03002$ a.u. The ground-state properties obtained from the FRPA are compared with quantum Monte Carlo results. The peak height in the static structure factor at $k=2k_{\rm F}$ depends significantly on the confinement model. These peaks are fitted with a function based on our finite wire-width theory demonstrating good agreement with FRPA.