Chern_simons Theory of the Anisotropic Quantum Heisenberg Antiferromagnet on a Square Lattice

We consider the anisotropic quantum Heisenberg antiferromagnet (with anisotropy $\lambda$) on a square lattice using a Chern-Simons (or Wigner-Jordan) approach. We show that the Average Field Approximation (AFA) yields a phase diagram with two phases: a Ne{\`e}l state for $\lambda>\lambda_c$ and a flux phase for $\lambda<\lambda_c$ separated by a second order transition at $\lambda_c \lambda_c$. We identify this transition with the isotropic Heisenberg point. It has a non-vanishing Ne{\` e}l order parameter, which drops to zero discontinuously for $\lambda<\lambda^*$.