New Developments in the Theory of Non-Magnetic Ground State and Magnetic-Field-Induced Spin Gap in Low Dimensional Spin Systems

利用解析和数值方法，研究了各种一维和准一维自旋系统的零或有限磁场基态。我们特别关注了零磁场和有限磁场下的自旋间隙态。我们提出了阶梯型有机自旋体系BIP-TENO在饱和磁化强度为1/4时磁场诱导自旋间隙的几种机制。我们已经成功地解释了观测到的磁化曲线的行为。本文采用解析和数值方法研究了畸变金刚石型自旋链，重点研究了零磁场和有限磁场下的基态。在这个系统中，根据量子参数的不同，出现了不同的相位。特别是在饱和磁化强度为1/3时，发现了磁化平台的变化机理。该模型很好地描述了蓝铜矿的磁性能。我们对键交替的自旋阶梯的相图得到了明确的结论。用三聚体性质、受挫性和自旋-自旋相互作用的XXZ各向异性这三个关键词发现了自旋系统的哈密顿量和波函数各向异性之间的反转现象。即，在量子参数的某些区域，尽管相互作用是类xy的，但仍实现了尼尔基态。当相互作用为类伊辛时，实现了自旋流体基态。我们澄清了F5PNN材料出现与晶格不相称的自旋有序性的条件。

By use of analytical and numerical methods, we have investigated the ground states with zero or finite magnetic fields for various one-dimensional and quasi-one-dimensional spin systems. Especially, we have focused on the spin-gap states in zero or finite magnetic fields.1. We have proposed several mechanisms for the magnetic-filed-induced spin gap at 1/4 of the saturation magnetization of a ladder type organic spin system BIP-TENO. We have succeeded to explain the behavior of the observed magnetization curve.2. We have studied the distorted diamond type spin chain, by use of analytical and numerical methods, especially focusing on the ground states in zero and finite magnetic field. In this system, there appears various phases depending upon the quantum parameters. In particular, it was found the change in the mechanism for the magnetization plateau at 1/3 of the saturation magnetization. The magnetic properties of azurite are well described by this model.3. We have obtained the definitive conclusion on the phase diagram of the spin ladder with the bond alternation.4. We have found the inversion phenomenon between the anisotropies of the Hamiltonian and the wave function for the spin systems with three keywords : trimer nature, frustration and the XXZ anisotropy of the spin-spin interactions. Namely, in some regions of the quantum parameters, the Neel ground state is realized in spite of the fact that the interactions is XY-like. And also, the spin-fluid ground state is realized when the interaction is Ising-like.5. We have clarified the condition for the appearance of the spin orderng which is incommensurate to the lattice for the material F5PNN.