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

低维量子海森堡模型基态的数值研究

基本信息

批准号：
07640503
负责人：
HIDA Kazuo
金额：
$ 1.47万
依托单位：
Saitama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1997
项目状态：
已结题

项目摘要

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

在这个为期三年的项目中，我们用数值方法研究了具有各种空间结构的低维量子Heiscnberg模型。主要结果如下：1.利用密度矩阵重整化群（DMRG）方法研究了链间弱相互作用下梯形量子海森堡模型的临界行为; 2.发展了一维随机量子系统的DMRG算法。在随机反铁磁量子海森堡模型中，证实了随机单态相的存在。利用DMRG方法研究了一维随机量子反铁磁Heisenberg模型在铁磁键存在下的低能行为。讨论了比热和磁化率随温度的变化关系。4.利用量子化学方法研究了一维随机量子反铁磁体 ...更多信息 DMRG方法。得到了基态能量、能隙分布和弦序与键交替的关系。5.利用量子Monte Carlo方法和一维玻色子系统的映射，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. 6.研究了具有2和4-自旋的各向同性一维海森堡模型的基态，得到了该模型的基态磁化强度随温度的变化规律.利用精确数值对角化方法研究了褶皱的空间周期性。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跃迁与自旋为1的反铁磁海森堡链的Haldane-二聚体跃迁之间的关系。利用改进的自旋波方法和二聚体展开方法研究了阻挫对自旋1/2双层量子反铁磁Heisenberg模型基态和激发谱的影响。结果表明，自旋能隙态在弱层间耦合下仍然存在。少