利用能级交叉和二聚化算符表征海森堡反铁磁系统的量子相变

Level Crossing and Dimerization Operator for Characterization of Quantum Phase Transition in the Heisenberg Antiferromagnet

用逆迭代计算阻挫自旋1/2海森堡反铁磁J_(1)-J_(2)方格子的基态和低激发态及相应的本征能量。在总自旋量子数的子空间中利用精确对角化和正交化波算符方法,得到哈密顿量H、总自旋量子数S、总自旋z分量量子数Sz_(T)的共同本征态。利用能级交叉和二聚化算符,分析了中间相量子相变点,讨论了自旋液态存在的区域。计算结果表明,按照无量纲参数g=J_(2)/J_(1),无序相分布在g=0.41~0.71,其两侧g=0.00~0.40和g=0.72~0.99分别为Neel相和条纹相。低激发自旋单态S=0和自旋三重态S=1的能级交叉将中间相分隔成g=0.41~0.49和g=0.50~0.71两个区域。在g=0.50~0.52的区域显示有低激发态二度简并的自旋单态存在,通过二聚化算符分析其自旋液态特征。

We present numerical inverse-iterative result for the ground state and the low-lying excitations and corresponding eigen-energies for the frustrated Spin-1/2 J_(1)-J_(2) Square Heisenberg Antiferromagnet.Using exact diagonalization and orthogonal wave-operator in the subspace of total spin,we obtain the common eigen-states among Hamiltonian H,total spin number S,and its z-component S_(T)^(z).Using level crossing and dimerization operator,we analyze the quantum phase transition point in the intermediate region,and discuss spin liquid regime as well.As revealed by the result,in the metric of dimensionless parameter g=J_(2)/J_(1),the nonmagnetic phase spreads in g=0.41~0.71,of which on the left and right sides are Neel and stripe phases for g=0.00~0.40 and g=0.72~0.99,respectively.The low-lying level crossing between the spin singlet S=0 and triplet S=1 separates the intermediate region as two regimes g=0.41~0.49 and g=0.50~0.71.Doubly degenerated spin singlets present in the low-lying excitations for g=0.50~0.52.Further,we use dimerization operator to analyze the characteristics of spin liquid in this regime.