Numerical Jordan-Wigner approach for two-dimensional spin systems

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 $\mathrm{}(S=1/2\mathrm{})\mathrm{}$ antiferromagnetic $\mathrm{XXZ}$ system as a function of the easy-axis anisotropy $\Delta$ on a periodic square lattice. For the $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}$ case the method converges to a Néel ordered ground state irrespective 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 such as frustrated or disordered systems.