Theoretical Study of Quantum-Spin Systems with Competing Interactions

本文研究了具有第一和第二近邻相互作用的一维晶格上自旋为1/2的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的，我们考虑了第一近邻相互作用是反铁磁的情况和第二近邻相互作用是铁磁的情况。(The前者和后者的情况分别称为情况AF和情况F。1.静态性质（1）基态性质：我们精确地计算了至多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，并将这些结果外推以估计无限尺寸极限中上述量的值。特别地，我们发现，随着第二近邻相互作用的增加，AF的基态经历了从没有能隙的自旋流体相到有有限能隙的二聚体相的相变， ...更多信息 两种相互作用都是各向同性的或具有XY型各向异性。(2)低温性能：用量子转移矩阵方法计算了内能和比热以及反关联长度和波数的温度依赖关系，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AF和F两种情况下，都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进行为的相互作用和温度依赖性。2.动力学性质我们研究了AF情况下的动力学性质，仅限于相互作用具有Ising型各向异性的情况。在伊辛极限的简并点附近，发现了Neel和（2，2）-反相态的孤子和二聚体态的三重态二聚体激发作为传播模式。这些激发也被发现占主导地位的动态自旋相关函数的中心峰的形状，通过与精确对角化方法获得的数值结果为12自旋的有限尺寸系统的比较。少

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