Behavior of a magnetic impurity in small metallic systems

主要工作如下：1.用量子蒙特卡罗方法研究了二维无序系统中的近藤效应。结果表明，局域磁矩被传导电子的自旋屏蔽或不屏蔽，取决于磁性杂质的位置。计算了局域力矩与传导电子自旋之间的关联函数。即使当局部力矩被完全屏蔽时，由于随机性，局部力矩附近的铁磁相关性也被抑制。当屏蔽不完全时，局域磁矩附近的反铁磁关联被强烈抑制。利用Bethe ansatz解研究了有限温度下Anderson模型和轨道简并Anderson模型的基元激发光谱。我们计算了元素激发光谱在混合价域…之间的交叉行为更多e和近藤政权。我们还计算了四方场和立方场等晶场中的元素激发光谱。结合热力学性质对实验结果进行了讨论。采用数值对角化方法和基于保角场论的有限尺寸尺度分析相结合的方法，系统地研究了磁场中各种一维自旋间隙系统的临界性质。我们计算了自旋关联函数的临界指数与磁场的关系。利用数值结果讨论了磁场中S=1/2两腿阶梯材料和霍尔丹带隙材料的核磁共振弛豫速率的实验结果。采用基于Lanczos算法的连分式方法，在磁化平台区计算了具有次近邻相互作用的S=1/2键交替链的动力学结构因子。结果与一维S=1/2XXZ模型的有效哈密顿量的精确激发谱进行了比较。较少

Results of the present project are summarized as follows :1. We investigated the Kondo effect in two-dimensional disordered systems using a quantum Monte Carlo method. It was shown that the local magnetic moment is screened or unscreened by the spin of the conduction electron, depending on the position of a magnetic impurity. The correlation function between the local moment and the spin of the conduction electron was also calculated. Even when the local moment is completely screened, the ferromagnetic correlation in the vicinity of the local moment is suppressed due to randomness. When the screening is incomplete, the antiferromagnetic correlation in the vicinity of the local moment is strongly suppressed.2. The elementary excitation spectrums for the Anderson model and the orbitally degenerate Anderson model were investigated at finite temperatures using the Bethe ansatz solution. We calculated a crossover behavior of the elementary excitation spectrums between the mixedvalence regim … More e and the Kondo regime. We also calculated the elementary excitation spectrums in crystalline fields such as tetragonal field and cubic field. Results were discussed in connection with thermodynamic quantities.3. Critical properties of various one-dimensional spin-gapped systems in magnetic fields were investigated systematically by combining a numerical diagonalization method and finite-size-scaling analysis based on conformal field theory. We calculated magnetic-field dependence of the critical exponent of the spin correlation function. Using the numerical results, we discussed the experimental findings concerning the NMR relaxation rates of the S=1/2 two-leg ladder material and the Haldane-gap material in magnetic fields.4. Using the continued fraction method based on Lanczos algorithm, the dynamical structure factor of the S=1/2 bond-alternating chain with a next-nearest-neighbor interaction was calculated at the magnetization-plateau region. Results were discussed in comparison with the exact excitation spectrums of an effective Hamiltonian ; one-dimensional S=1/2XXZ model. Less