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

我们研究了一维晶格上具有第一和第二近邻相互作用的自旋1/2海森堡磁体的静态和动态性质。假设第二近邻相互作用是反铁磁性的，我们考虑了第一近邻相互作用是反铁磁性的情况以及第一近邻相互作用是铁磁性的情况。(前一种情况和后一种情况分别称为情况AF和情况F)1.静态性质(1)基态性质：我们精确地计算了多达20个自旋的有限大小系统的能量、单三重态能隙、自旋关联函数和磁化强度，并对这些结果进行了外推，以估计这些量在无限大小的极限中的值。特别是，我们发现随着次邻相互作用大小的增加，在AF的情况下，基态经历了从无能隙的自旋-流体相到有限能隙的二聚体相的相变，其中…(2)有限温度性质：用量子传输矩阵方法计算了内能和比热以及反关联长度和波数随温度的变化关系，并由此描述了自旋关联函数在长程极限下的渐近行为。我们发现，在F和AF两种情况下，都存在无序线的量子模拟，它描述了长距离范围内自旋关联函数的渐近行为的相互作用和温度依赖关系。动力学性质我们研究了CASE AF的动力学性质，将自己限制在相互作用具有伊辛型各向异性的情况下。在伊辛极限的简并点附近，发现了处于Neel态和(2，2)-反相态的孤子以及处于二聚态的三重态-二聚体激发作为传播模。通过与有限自旋12自旋系统的精确对角化方法所得到的数值结果的比较，还发现这些激发对动态自旋关联函数中中心峰的形状起主导作用。较少

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》。

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；

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

原田功；