Correlation effects in one-dimensional metallic quantum wires under various confinements
Vidit Gangwar, Vinod Ashokan, Ankush Girdhar +3 more
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 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 s . 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 V 1 ( q ) (harmonic), V 2 ( q ) (cylindrical), and V 5 ( q ) (harmonic-delta) approaches ε c ( r s ) = − π 2 / 360 ∼ − 0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, ; V. Ashokan, , ]. 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 ε c ∼ − 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 ) ,
arXiv:2507.17925•Physical review. B./Physical review. B•Dec 9, 2025•2 citations