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成员迄今为止取得的成果，而且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全球观点。关于今年的研究成果，我们发表了许多论文，并正在研究新的课题，这些课题将在明年发表。在这里，我们报告的一些结果。（1）关于推广到SU（N）自由度偏离的超对称t-J模型中简单激发谱的性质，注意到Gutzwiller波函数的置换性质与自由电子的置换性质相同，从而获得了一个清楚的认识。在Sutherland模型中，通过对相互作用强度的特殊选择，系统得到了与Kawakami的分数量子Hall（FractionalQuantumHall）系统中边缘态的相似性。本文提出了一个新的手征模型 关于我们 线，并推导出它的精确性质（Kawakami和Kuramoto）在一维安德森格，特殊的参数选择可以导致精确的解决方案（Vollhardt）。此外，我们提出了一个新的超对称连续介质模型及其精确解（Kuramoto和Zittartz）。尤其是最后一项研究，这个项目的研究之旅是必不可少的。(2)In由于Hubbard模型是高维的极限，它被认为是自洽介质中的有效安德森杂质。已通过严格方法（Vollhardt）研究了该限度内的杂质效应。利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-绝缘体转变（Kuramoto）附近发现了一个新的能量标度。（3）在RVB图象的基础上研究了二维t-J模型的动力学。动力学磁化率已被计算与使用从玻色子平均场理论的超导转变（福山）以上和以下。结果再现了中子散射的实验结果。在平均场理论之外的进一步研究已经开始考虑波动（Woelfle）。（4）用NRG（Shiba）对超导体中的磁性杂质进行了研究。与以前的近似理论的关系已经澄清（Shiba，Mueller-Hartmann，Zittartz）。为了讨论在严格的基态下铁磁性的发生，研究了含空穴的Hubbard模型的基态，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