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We present a detailed comparison of the self-consistent calculations based onthe Hartree-Fock and the spin density functional theory for a spit-gate quantumwire in the IQH regime. We demonstrate that both approaches providequalitatively (and in most cases quantitatively) similar results for thespin-resolved electron density, spin polarization, spatial spin separation atthe edges and the effective $g$ factor. The both approach give the same valuesof the magnetic fields corresponding to the successive subband depopulation andqualitatively similar evolution of the magnetosubbands. Quantitatively,however, the HF and the DFT subbands are different (even though thecorresponding total electron densities are practically the same). In contrastto the HF approach, the DFT calculations predict much larger spatial spinseparation near the wire edge for the low magnetic fields (when thecompressible strips for spinless electrons are not formed yet). In the oppositelimit of the large fields, the Hatree-Fock and the DFT approaches give verysimilar values for the spatial spin separation.

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