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

我们研究了具有第一和第二邻域相互作用的一维晶格上自旋 1/2 海森堡磁体的静态和动态特性，假设第二邻域相互作用是反铁磁的，我们考虑了第一邻域相互作用的情况。 - 相邻相互作用是反铁磁的和铁磁的情况（前者和后者分别称为情况AF和情况F。） 1．性质(1) 基态性质：我们精确计算了最多 20 个自旋的有限尺寸系统的能量、单重态-三重态能隙、自旋相关函数和磁化强度，并推断这些结果来估计特别是，我们发现，随着第二邻域相互作用强度的增加，AF 中的基态会从没有能隙的自旋流体相发生相变。到二聚体相有限能隙，其中两个相互作用都是各向同性或具有 XY 型各向异性。 (2) 有限温度性质：利用量子转移矩阵方法，我们计算了内能和比热的温度依赖性，还有反相关长度和波数，这两者都描述了自旋相关函数在长距离极限下的渐近行为，我们发现，在情况 AF 和情况 F 下，存在无序线的量子模拟，它表征了长距离极限下自旋相关函数渐近行为的相互作用和温度依赖性。 2．动态性质我们研究了AF的动态性质，仅限于该情况。其中相互作用具有伊辛型各向异性，靠近伊辛极限的简并点，孤子处于尼尔态和 (2,2)-反相态，三线态二聚体激发。通过与有限尺寸系统的精确对角化方法获得的数值结果进行比较，还发现这些激发态在动态自旋相关函数中主导着中心峰的形状。少旋转 12 次。

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。

Takashi Tonegawa; Isao Harada: "Ground-State Properties of the One-Dimensional Isotropic Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions" Journal of the Physical Society of Japan. 56. 2153-2167 (1987)

利根川隆；

五十嵐潤一、利根川孝: Physical Review B.

Junichi Igarashi、Takashi Tonekawa：物理评论 B.

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；