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，使用Metho进行了各种结构的低维量子Heiscnberg，总结了主要结果如下：1。研究了梯子量子量子的临界行为，以较弱密度基质重量化组（DMRG）方法。2。Thod.2.开发了一个dimensil antum antum antum系统的DMRG方法。系统正在进行中。3。一个身分随机量子抗铁磁的低能Heisenberg He存在铁磁键是DMRG方法。使用...的量子抗铁磁铁，使用...悬挂式分布和弦序的降序。使用量子蒙特卡洛法和映射一维的bostem。使用确切的数值进行了量子计算相图和临界指数。旋转-2/2/2/2 bilayr量子抗磁性的海森贝格使用修饰的自旋方法和二聚体膨胀方法降低到弱层偶联的极限。