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3年的项目中，已经使用数值方法研究了具有各种空间结构的低维量子Heiscnberg模型。主要结果总结如下：1。使用密度矩阵重新归一化组（DMRG）方法，研究了梯子量子量子量子的临界行为。2。开发了DMRG方法的算法。随机的抗铁磁量子Heisenberg模型中验证了随机单相的存在。 3.使用DMRG方法研究了铁磁键的情况下，一维随机量子抗铁磁模型模型的低能量行为正在进行中。讨论了特定的热和磁敏感性的温度依赖性。4。使用…更多的是DMRG方法，研究了具有键替代方案的一维随机量子抗铁磁铁。获得了Grund状态能，间隙分布和弦顺序的键抗依赖性。结果表明，旋转旋转的不稳定性被随机性抑制。使用精确的数值诊断方法研究了空间周期性。计算相图和临界指数。 Spin-1/2抗磁性Heisenberg链的尺寸转变与Spin-1抗磁性Heisenberg链的Haldane-Dimer Transition之间的关系。 7.挫败感对Spin-1/2 bilayr量子抗磁性Heisenberg模型的基态和兴奋谱的影响正在进行中。发现自旋间隙状态的生存到弱层偶联的极限。较少的