  We present systematic quantitative description of the magnetoconductance of
the split-gate quantum wires. Accounting for the exchange and correlation
interactions within the spin density function theory (DFT) leads to the lifting
of the spin degeneracy and formation of the spin-resolved plateaus at odd
values of $e^{2}/h$. We show that the width of the odd conductance steps in the
spin DFT calculations is equal to the width of the transition intervals between
the conductance steps for the spinless electrons in the Hartree approximation.
A detailed analysis of the structure of compressible/incompressible strips and
the evolution of the Hartree and the spin-DFT subband structure provides an
explanation of this finding. Our spin-DFT calculations reproduce not only
qualitatively, but rather quantitatively all the features in the
magnetoconductance observed in the recent experiment (I. P. Radu, J. B. Miller,
S. Amasha, E. Levenson-Falk, D. M. Zumbuhl, M. A. Kastner, C. M. Marcus, L. N.
Pfeiffer, and K. W. West, to be published) including the unexpected effect of
the collapse of the odd conductance plateaus at lower fields.
