  We present a numerical self consistent variational approach based on the
Jordan-Wigner transformation for two dimensional spin systems. We apply it to
the study of the well known quantum (S=1/2) antiferromagnetic XXZ system as a
function of the easy-axis anisotropy \Delta on a periodic square lattice. For
the SU(2) case the method converges to a N\'eel ordered ground state
irrespectively of the input density profile used and in accordance with other
studies. This shows the potential utility of the proposed method to investigate
more complicated situations like frustrated or disordered systems.
