Numerical Study of the Ground States of the Low Dimensional Quantum Heisenberg Models

在这个为期3年的项目中，采用数值方法研究了具有不同空间结构的低维量子海森堡模型。主要研究结果总结如下：利用密度矩阵重整化群（DMRG）方法研究了阶梯量子Heisenberg模型在弱链间相互作用极限下的临界行为。提出了一维随机量子系统的DMRG方法的算法。在随机反铁磁量子海森堡模型中验证了随机单重态相的存在性。在准周期系统中的应用正在进行中。利用DMRG方法研究了一维随机量子反铁磁海森堡模型在铁磁键存在下的低能行为。讨论了比热和磁化率的温度依赖性。利用DMRG方法研究了具有键交替的一维随机量子反铁磁体。得到了基态能量、间隙分布和弦序的键交替依赖关系。结果表明，随机可以抑制自旋-佩尔斯不稳定性。利用量子蒙特卡罗方法研究了一维铁磁-反铁磁交替海森堡模型的有限温度磁化过程，并将其映射到一维玻色子系统上。采用精确数值对角化方法研究了具有2倍和4倍空间周期的各向同性一维海森堡模型的基态。计算了相图和临界指数。阐明了自旋为1/2的反铁磁海森堡链的二聚化转变与自旋为1的反铁磁海森堡链的卤代二聚体转变之间的关系。各向异性与磁场影响的研究正在进行中。采用改进的自旋波法和二聚体展开法研究了受挫对自旋1/2双层量子反铁磁海森堡模型基态和激发谱的影响。发现自旋隙态一直存在到弱层间耦合的极限。少

In this 3-year project, the low dimensional quantum Heiscnberg models with various spatial structures have been investigated using numerical methods. The main results are summarized as follows :1.The critical behavior of the ladder quantum Heisenberg model is studied in the limit of weak interchain interaction using the density matrix renormalization group (DMRG) method.2.The algorithm of the DMRG method for one-dimensional random quantum systems is developed. The existence of the random singlet phase is verified in the random antiferromagnetic quantum Heisenberg model. The application to the quasi-periodic systems is in progress.3.The low energy behavior of the one-dimensional random quantum antiferromagnetic Heisenberg model in the presence of the ferromagnetic bonds is investigated using the DMRG method. The temperature dependence of the specific heat and magnetic susceptibility is discussed.4.The one-dimensional random quantum antiferromagnet with bond alternation is studied using … More the DMRG method. the bond-alternation-dependence of the grund state energy, gap distribution and the string order is obtained. It is shown that the spin-Peierls instability is suppressed by randomness.5.The finite temperature magnetization process of the one-dimensional ferromagnetic-antiferromagnetic alternating Heisenberg model is investigated using the quantum Monte Carlo method and the mapping onto the one-dimensional boson system.6.The ground state of the isotropic one-dimsnaional Heisenberg model with 2 and 4-fold spatial periodicity is investigated using the exact numerical diagoualization method. The phase diagram and the critical exponents are calculated. The relationship between the dimerization transition of the spin-1/2 antiferromagnetic Heisenberg chain and the Haldane-dimer transition of the spin-1 antiferromagnetic Heisenberg chain is clarified. The study of the effect of the anisotropy and magnetic field is in progress.7.The effect of frustration on the ground state and excitation spectrum of the spin-1/2 bilayr quantum antiferromagnetic Heisenberg model is studied using the modified spin wave method and the dimer expansion method. It is found that the spin gap state survives down to the limit of weak interlayr coupling. Less