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

我们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场和有限磁场基态。特别是，我们重点研究了零磁场和有限磁场中的自旋能隙态。我们提出了几种机制来解释梯形有机自旋系统BIP-Teno在饱和磁化强度1/4处的磁场诱导自旋能隙。我们成功地解释了观察到的磁化曲线的行为。我们用解析和数值的方法研究了扭曲的钻石型自旋链，特别是零场和有限磁场中的基态。在这个系统中，根据量子参数的不同，会出现不同的位相。特别是在饱和磁化强度的1/3处发现了磁化平台机制的变化。该模型较好地描述了天青石的磁性。得出了自旋阶梯随键变化的相图的确凿结论。我们发现了自旋系统的哈密顿各向异性和波函数之间的反转现象，这三个关键字是：三聚体性质、受挫和自旋-自旋相互作用的XXZ各向异性。也就是说，在量子参数的某些区域，尽管相互作用是类xy的，但还是实现了Neel基态。并且，当相互作用是类伊辛相互作用时，实现了自旋-流体基态。我们阐明了F5PNN材料出现与晶格不相称的自旋有序的条件。

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.