Schwinger-Boson Mean Field Solution of Spin-1 (or 1/2) 2D Anisotropic Heisenberg Antiferromagnet

Using the Resonant Valence Bond (RVB) concept and the Schwinger-boson mean field approximation, we investigate a two dimensional anisotropic Heisenberg antiferromagnet. We find that increasing the coupling ratio ($\alpha=J_{y}/J_{x}$), a disordered-ordered phase transition appears beyond a critical value ($\alpha_{c}$). When $\alpha>\alpha_{c}$ there exists a finite $T_{N}$ beyond which an ordered-disordered phase transition occurs, while for $\alpha<\alpha_{c}$ there always exists a gap. Also we find that a decoupling temperature $T_{D}$ exists for 1D and 2D isotropic case, when $T$ approaches $T_{D}$ the RVB order parameter decreases rapidly to zero.