Theoretical Study of Quantum-Spin Systems with Competing Interactions

具有竞争相互作用的量子自旋系统的理论研究

• 批准号: 61540265
• 负责人: TONEGAWA Takashi
• 金额: $ 1.09万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540265/
• 关键词: One-Dimensional Quantum-Spin System; Competing Interactions; Static Properties; Dynamic Properties; Ground-State Properties; Finite-Temperature Properties; Exact Diagonalization Method for Finite-Size Systems; 量子転送行列法; 有限温度における性質; soliton型素励起; t

We have studied the static and dynamic properties of the spin-1/2 Heisenberg magnet on the one-dimensional lattice with first- and second-neighbor interactions. Assuming that the second-neighbor interaction is antiferromagnetic, we have considered the case where the first-neighbor inter-action is antiferromagnetic and the case where it is ferromagnetic. (The former and latter cases are called case AF and case F, respectively.)1. static Properties(1) Ground-state properties: We have calculated exactly the energy, the singlet-triplet energy gap, the spin correlation function, and the magnetization for finite-size systems of up to 20 spins, and have extrapolated these results to estimate the values of the above quantities in the infinite-size limit. In particular, we have found that with increasing magnitude of the second-neighbor interaction the ground state in case AF undergoes a phase transition from the spin-fluid phase with no energy gap to the dimer phase with finite energy gap, whe … More n both interactions are isotropic or have the XY-type anisotropy.(2) Finite-temperature properties: Using the quantum transfer matrix method, we have calculated the temperature dependence of the internal energy and the specific heat and also that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the spin cor-relation function in the long-distance limit is described. We have found that, both in case AF and case F, there exists a quantum analog of the disorder line which characterizes the interaction and temperature dependence of the asymptotic behavior of the spin correlation function in the long-distance limit.2. Dynamic PropertiesWe have investigated the dynamic properties of case AF, confining ourselves to the case where the interactions have the Ising-type anisotropy. Near the degenerate point in the Ising limit, solitons in the Neel and (2,2)-antiphase states and triplet-dimer excitations in the dimer state have been found as propagating modes. These excitations have also been found to dominate the shape of the central peak in the dynamic spin correlation function, through the comparison with the numerical results obtained by an exact diagonalization method for a finite-size system of 12 spins. Less

我们已经在具有第一和第二邻络相互作用的一维晶格上介绍了Spin-1/2 Heisenberg磁铁的静态和动态性能。假设第二个邻居相互作用是抗铁磁磁性的，我们认为第一邻二邻磁相互作用是抗磁磁性的，而它是铁磁性的情况。 （前者和后来的案例分别称为病例AF和案例F。）1。静态特性（1）地面属性：我们已经精确地计算了能量，单三块能量间隙，自旋相关函数以及最多20个自旋的有限尺寸系统的磁化，并推断了这些结果，以估计无限大小限制中上述量的值。特别是，我们发现，随着第二个neighbor相互作用的幅度越来越大，如果AF发生从自旋流通相的相变，没有能量间隙，且具有有限的能量间隙，而不是有限的能量差距，则更多的N相互作用是等于XY型的andpe Anisotropy的同型相互作用。内部能量和特定的热量以及逆相关长度和波数的热量，通过这两者都描述了旋转COR相关函数在长距离极限中的不对称行为。我们发现，在AF和病例F中，存在疾病线的量子类似物，该量子类似物表征了自旋相关函数的不对称行为的相互作用和温度依赖性在长距离限制下。2。动态属性我们已经研究了病例AF的动态特性，将自己局限于相互作用具有ISING型各向异性的情况。在ISing极限的退化点附近，Neel和（2,2） - Antiphase状态的实体和二聚体状态下的三重态兴奋是繁殖模式。还发现这些兴奋是通过与通过精确的12旋转有限尺寸系统获得的精确对角线化方法的数值结果进行比较，在动态自旋相关函数中主导了中央峰的形状。较少的

项目成果

利根川孝,原田勲: Journal of the Physical Society of Japan.

利根川隆、原田勋：日本物理学会杂志。

利根川孝、原田勲: Physica(Utrecht).

利根川隆、原田功：Physica（乌得勒支）。

利根川孝、原田勲: Journal de Physique.

利根川隆、原田功：《体质杂志》。

Isao Harada; Tetsuji Kimura; Takashi Tonegawa: "Disorder Line in a Quantum Spin Chain with Competing Interactions" Journal de Physique (Paris).

原田功；

Takashi Tonegawa; Isao Harada: "Ground-State Properties of the One-Dimensional Spin-1/2 Heisenberg-XY Antiferromagnet with Competing Interactions" Journal de Physique (Paris).

利根川隆；