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

这一国际研究项目不仅使我们能够讨论成员们迄今所取得的成果，而且使我们能够发起新的合作研究。通过这种系统的合作，我们正在建立一个基于不同但相关的系统和方法的结果的共同的全球观点。根据今年的研究结果，我们发表了许多论文，并正在研究新的主题，这些主题将在明年发表。本文报道了一些结果：(1)关于推广到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Gutzwiter波函数的排列性质与自由电子(Kuramoto)的排列性质是相同的，从而获得了明确的认识。在特殊选择相互作用强度的Sutherland模型中，系统类似于分数量子霍尔(FQH)系统(Kawakami)中的边态。我们在这个…中提出了一个新的手性模型在一维Anderson格子中，参数的特殊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介质模型及其精确解(Kuramoto和Zittartz)。在高维极限下，Hubbard模型被认为是自洽介质中有效的Anderson杂质。用严格的方法(Vollhardt)研究了这一极限内的杂质效应。用数值重整化群方法(NRG)计算了态密度、磁化率、比热等物理量，并在金属-绝缘体相变(Kuramoto)附近发现了一个新的能量标度。(3)在RVB图的基础上研究了二维t-J模型的动力学。在超导相变(Fukuyama)上方和下方用从属玻色子平均场理论计算了动力学极化率。结果重现了中子散射的实验结果。除了平均场理论之外，还开始了对涨落的进一步研究(Woelfle)。(4)利用NRG(Shiba)对超导体中磁性杂质的研究结果进行了综述。与以前的近似理论(Shiba，Mueller-Hartmann，Zittartz)的关系已被阐明。为了讨论严酷地面上铁磁性的发生，我们研究了具有微孔的Hubbard模型的基态，并特别注意了晶格类型(Mueller-Hartmann)的影响。较少

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