Theory of collective behavior in condensed matter systems---low- and high-dimensions

这一国际研究项目使我们不仅能够讨论各成员迄今取得的成果，而且能够开展新的合作研究。通过这种系统的合作，我们正在建立一种共同的全球观点，这种观点以不同但相关的系统和方法的结果为基础。关于今年的研究成果，我们已经发表了许多论文，并且正在研究新的课题，明年将发表。下面我们报道其中的一些结果。(1)关于扩展到SU(N)自由度的超对称t-J模型中简单激发谱的性质，通过注意到Gutzwiller波函数的排列性质与自由电子的排列性质相同（Kuramoto），获得了清晰的认识。在具有特殊相互作用强度选择的Sutherland模型中，系统获得了与分数量子霍尔（FQH）系统（Kawakami）中的边缘态相似的状态。我们在这条线中提出了一个新的手性模型，并推导了它的精确性质（Kawakami和Kuramoto）。在一维Anderson晶格中，特殊的参数选择可以得到精确解（Vollhardt）。此外，我们还提出了一个新的超对称连续统模型及其精确解（Kuramoto和Zittartz）。特别是在最后的学习中，这个项目的研究之旅是必不可少的。(2)在高维极限下，Hubbard模型被认为是自洽介质中有效的Anderson杂质。杂质对这个极限的影响已经用一种严格的方法进行了研究（Vollhardt）。利用数值重整化群法（NRG）计算了态密度、磁化率、比热等物理量，并在金属-绝缘体跃迁附近确定了一个新的能量标度（Kuramoto）。(3)在RVB图像的基础上，研究了二维t-J模型的动力学。利用从玻色子平均场理论计算了超导跃迁以上和以下的动力学磁化率（Fukuyama）。结果与中子散射实验结果吻合。在平均场理论之外，对波动的解释已经开始了进一步的研究（Woelfle）。(4)利用NRG （Shiba）对超导体中的磁性杂质进行了研究。澄清了与以往近似理论的关系（Shiba, Mueller-Hartmann, Zittartz）。为了讨论铁磁性在严格的地面上的发生，我们研究了带有轻微空穴的Hubbard模型的基态，并特别注意了晶格类型（Mueller-Hartmann）的影响。少

This international research project has enabled us not only to discuss on members' results so far obtained, but to initiate new cooperative researches. By this systematic cooperation, we are in the course of building a common global point of view which is based on results from different but related systems and methods.Concerning the results of research for this year, we have published many papers and are working on new topics which will be published in the next year. Here we report on some of the results.(1)Concerning the nature of simple excitation spectra in the supersymmetric t-J model extended to SU(N) digress of freedom, a clear insight has been gained by noting that the permutation property of the Gutzwiller wave function is the same as that of free electrons (Kuramoto). In the Sutherland model with special choice of interaction strength, the system gets a similarity to edge states in the fractional quantum Hall (FQH) system (Kawakami). We have proposed a new chiral model in this … More line and derived its exact properties (Kawakami and Kuramoto) In the one-dimensional Anderson lattice, special choice of the parameters can lead to the exact solution (Vollhardt). Furthermore, we have proposed a new supersymmetric continuum model and its exact solution (Kuramoto and Zittartz). Especially for the last study, the research trip by this program was indispensable.(2)In the limit of high dimensions, the Hubbard model is regarded as an effective Anderson impurity in a self-consistent medium. Impurity effects in this limit has been studied by a rigorous method (Vollhardt). With use of the numerical renormalization group method (NRG), quantities such as the density of states, susceptibility, specific heat has been calculated and a new energy scale has been identified near the metal-insulator transition (Kuramoto).(3)Dynamics of the two-dimensional t-J model has been studied on the basis of the RVB picture. The dynamical susceptibility has been calculated with use of the slave-boson mean-field theory both above and below the superconducting transition (Fukuyama). The results reproduce experimental results of neutron scattering. Further study beyond the mean-field theory has been initiated with account of fluctuations (Woelfle).(4)Survey of results has been given on magnetic impurities in a superconductor with use of the NRG (Shiba). Relationship with previous approximate theories has been clarified (Shiba, Mueller-Hartmann, Zittartz). In order to discuss the occurrence of ferromagnetism on a rigorous ground, the ground state of the Hubbard model with slight holes has been studied with special attention to the influence of lattice types (Mueller-Hartmann). Less