二维各向异性海森伯反铁磁性的Schwinger-Boson平均场解法

SCHWINGER-BOSON MEAN FIELD SOLUTION OF SPIN S=1(OR 1/2)2D ANISOTROPIC HEISENBERG ANTIFERROMAGNET

运用共振价键概念和Schwinger-Boson平均场近似,研究了二维正方格子上的各向异性Heisenberg反铁磁性。结果表明,耦合率α=J_y/J_x达到临界值α_0时,系统发生有序一无序相变;α>α_0时,温度超过T_N(Nèel温度),发生有序一无序相变;α<α_0时,系统存在能隙,各向同性的一维和二维系统具有共同的失耦温度T_D。当温度接近T_D时,共振价键序参量迅速减为零。

Using the Resonant Valence Bond (RVB) concept and the Schwinger-Boson Mean Field approximation, this paper investigates a two dimensional (square lattice) anisotropic Heisenberg antiferromagnet. By increasing the coupling ratio (α=J_y/J_x), a disor- der-order phase transition will appear beyond a critical value(α_0). When α>α_0 there exists a temperature T_N beyond which an order-disorder phase transition will occur, while for α<α_0 there always exists an energy gap. A constant T_D (decoupling temperature) of a certain spin value system exists for 1D and 2D isotropic case. When T approaches T_D the RVB order parameter decreases rapidly to zero.