Quantum wires in magnetic field: A comparative study of the Hartree-Fock and the spin density functional approaches

TL;DR

This study compares Hartree-Fock and spin density functional theory methods for quantum wires in magnetic fields, showing they produce similar qualitative results but differ quantitatively in certain aspects like subband energies and spin separation.

Contribution

It provides a detailed comparison of HF and DFT approaches for quantum wires, highlighting their similarities and differences in predicting electronic and spin properties under magnetic fields.

Findings

Both methods yield similar spin-resolved densities and g-factors.

DFT predicts larger spin separation at low magnetic fields.

Quantitative differences exist in subband energies despite similar total densities.

Abstract

We present a detailed comparison of the self-consistent calculations based on the Hartree-Fock and the spin density functional theory for a spit-gate quantum wire in the IQH regime. We demonstrate that both approaches provide qualitatively (and in most cases quantitatively) similar results for the spin-resolved electron density, spin polarization, spatial spin separation at the edges and the effective $g$ factor. The both approach give the same values of the magnetic fields corresponding to the successive subband depopulation and qualitatively similar evolution of the magnetosubbands. Quantitatively, however, the HF and the DFT subbands are different (even though the corresponding total electron densities are practically the same). In contrast to the HF approach, the DFT calculations predict much larger spatial spin separation near the wire edge for the low magnetic fields (when the compressible strips for spinless electrons are not formed yet). In the opposite limit of the large fields, the Hatree-Fock and the DFT approaches give very similar values for the spatial spin separation.