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Springer proceedings in physics

Correlation Effects in Quasi-One-Dimensional Quantum Wires Under Transverse Confinement of an Infinite Square Well

Vinod Ashokan, Vidit Gangwar, Gautam Shah, Renu Bala

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-981-92-1538-6_4

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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 ) ,
We investigate the scattering and two-body bound states of two ultracold atoms in a quasi-two-dimensional (quasi-2D) confinement, with the confinement potential being an infinitely deep square well (box potential) in the transverse (zzz) direction, and the motion of the atoms in the $x\text{\ensuremath{-}}y$ plane being free. Specifically, we calculate the effective 2D scattering length and 2D effective range parameter of the low-energy scattering, as well as the energy and the transverse-excited-mode probability of the bound states. Comparing these results with those obtained under a harmonic transverse confinement potential, which has the same characteristic length as the box potential, we find that in most of the cases the 2D effective range parameter for the box confinement is approximately 0.28 of the one for the harmonic confinement. Moreover, the transverse-excited-mode probability of the bound states for the box confinement is also much lower than the one for the harmonic confinement. These results suggest that the transverse excitation in the box confinement is notably weaker than the one in the harmonic confinement with the same characteristic length. Therefore, achieving quasi-2D ultracold gases well described by pure-2D effective models, particularly those with 2D contact interaction, is more feasible through box confinement. Our results are helpful for the quantum simulation of 2D many-body physics with ultracold atoms, e.g., the suppression of 2D effective range parameter may lead to an enhancement of quantum anomaly in two-dimensional Fermi gases. Additionally, our calculation method is applicable to the two-body problems of ultracold atoms in other types of quasi-2D confinements.