Calculation of Raman Spectra in Quantum Antiferromagnetic Systems containing Spin Gaps

量子效应有一种隐藏在经典性质阴影中的倾向。然而，我们可以直接在反铁磁材料中发现量子效应，因为自旋之间的交换相互作用对量子性质的形成起着至关重要的作用。近年来，“量子反铁磁性”在低维体系中得到了广泛的关注，例如过渡金属氧化物化合物的层型晶体。在这些系统中，基态是由单线态二聚体形成的。这些状态本质上有能量间隙，称为“自旋间隙”。为了探测这些自旋间隙，被称为“磁拉曼光谱”的非弹性光散射过程的实验具有很大的影响。本研究对反铁磁材料中由磁激发引起的光学性质进行了理论计算。特别地，我们对有限数的自旋系统进行了精确对角化。本计算给出了本征值和本征向量的数值计算结果，它们在量子反铁磁系统的特征特征方面具有相当丰富的信息。实际上，我们在计算中对拉曼光谱进行了再现。进一步，用数值方法得到了自旋过程中的空间相关函数。结果表明在这些体系中存在新磁相的可能性。此外，本研究还与姜-泰勒效应密切相关，因为它涉及到磁性表现的基本机制问题。因此，我们研究了这些量子反铁磁化合物的扬-泰勒效应与光谱之间的关系。在研究的延伸过程中，我们得到了出现在磁g因子中的“量子混沌”效应的观点。这为我们提供了一个相当现实的“量子混沌”模型，以及研究磁性的新线索。此外，近年来原子气体中玻色凝聚实验研究的发展，也为我们提供了这种量子凝聚系统所共有的新模型。因此，我们积极地研究原子气体中的玻色凝聚与琼-泰勒效应中“量子混沌”发生过程的关系。少

The quantum effects have a tendency of being hidden in the shadow of classic natures. However, we can find directly quantum effects in antiferromagnetic materials, because the exchange interaction between spins plays an essential role to making quantum natures. Recently, much attention has been paid to "quantum antiferromagnetism" in the low-dimensional systems, for example layer type crystals of Transition-metal oxide compounds. In those systems, ground states are made by singlet dimers. This states have essentially energy gaps, which are called "spin gaps". In order to detect these spin gaps, the experiments of the non-elastic light-scattering process called "magnetic Raman spectrum" are quite influential.This research makes the theoretical calculation for the optical properties originating from magnetic excitations in antiferromagnetic materials. In particular, we make the exact diagonalization in the spin systems for finite numbers. This calculation gives eigenvalues and eigenvectr … More os numerically, which have quite fruitful information in characteristic features of quantum antiferromagnetic systems. In fact, we make the reproduction of Raman spectrum in calculation. Further, spatial correlation functions during spins are obtained numerically. The results suggest us the possibility of new magnetic phases in those systems. Moreover, this research is related closely to Jahn-Teller effect as the problem which concerns the basic mechanism giving the manifestation of the magnetism. Therefore, we examine the relationship between Jahn-Teller effect and the optical spectrum for those quantum antiferromagnetc compounds. In the extension process of the research, we get the viewpoint of the effect caused by "the quantum chaos", which appears in the magnetic g factor. This leads us one of the quite realistic models of "quantum chaos", as well as the new clue to investigations of magnetism. In addition, the developing of the recent experimental research for Bose-condensations in atomic gases gives us the new model which is common to such the quantum-condensed systems. Therefore, we attack actively the problem of Bose-condensations in atomic gases in relation with the process of the occurrence "quantum chaos" in Jahn-Teller effect. Less