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

凝聚态系统集体行为理论——低维和高维

• 批准号: 05044201
• 负责人: KURAMOTO Yoshio
• 金额: --
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Overseas Scientific Survey.
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05044201/
• 关键词: t-J Model; Supersymmetry; Anderson lattice; Edge states; Copper oxides; Superconductivity; Kondo effect; Nagaoka problem

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

这个国际研究项目使我们不仅能够讨论成员迄今取得的成果，而且能够启动新的合作研究。通过这种系统性的合作，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。关于今年的研究成果，我们已经发表了许多论文，并正在研究明年将发表的新课题。这里我们报告一些结果。(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)，获得了清晰的见解。在具有特殊相互作用强度选择的 Sutherland 模型中，系统与分数量子霍尔 (FQH) 系统 (Kawakami) 中的边缘态相似。我们在此系列中提出了一种新的手性模型，并推导了其精确性质（Kawakami 和 Kuramoto）。在一维安德森晶格中，参数的特殊选择可以得出精确的解（Vollhardt）。此外，我们提出了一种新的超对称连续介质模型及其精确解（Kuramoto 和 Zittartz）。尤其是最后的研究，本课题的考察之旅是不可或缺的。(2)在高维极限下，哈伯德模型被视为自洽介质中的有效安德森杂质。已通过严格的方法（Vollhardt）研究了该限值中的杂质影响。利用数值重正化群方法(NRG)，计算了态密度、磁化率、比热等量，并在金属-绝缘体转变附近(Kuramoto)识别了新的能量尺度。(3)基于RVB图研究了二维t-J模型的动力学。使用从玻色子平均场理论计算了超导转变之上和之下的动力学磁化率（福山）。结果再现了中子散射的实验结果。考虑了波动（Woelfle），已经开始了超越平均场理论的进一步研究。（4）使用NRG（Shiba）对超导体中的磁性杂质进行了结果调查。与先前近似理论的关系已得到澄清（Shiba、Mueller-Hartmann、Zittartz）。为了讨论严格基态上铁磁性的发生，研究了带有小孔的哈伯德模型的基态，特别关注晶格类型的影响（Mueller-Hartmann）。较少的

项目成果

H.Shiba: "Quantum Monte Carlo Methods in Condensed Matter Physics" World Scientific, 11 (1993)

H.Shiba：“凝聚态物理中的量子蒙特卡罗方法”《世界科学》，11 (1993)

H.Shiba: World Scintific. Recent Advances in Magnetism of Transition Metal Compounds, 372-381 (1993)

H.Shiba：世界科学。

Th.Hanisch: "Ferromagnetism in the Hubbard Model : Instability of the Nagaoka State on the Square Lattice" Ann.Phys.2. 381-397 (1993)

Th.Hanisch：“哈伯德模型中的铁磁性：方形晶格上长冈态的不稳定性”Ann.Phys.2。

V.Janis: "Construction of analytically Tractable Mean-field Theories for Quantum Models. I. General Formalism with Application to the Hubbard Model at Strong Coupling" Z.Phys.B, Condens.Matter. 91. 317-323 (1993)

V.Janis：“量子模型的分析易处理平均场理论的构建。I. 强耦合哈伯德模型的一般形式主义”Z.Phys.B，Condens.Matter。

T.Tanamoto: "Magnetic Properties of Extended t-J Model I" J.Phys.Soc.Jpn.62. 717-730 (1993)

T.Tanamoto：“扩展 t-J 模型 I 的磁性”J.Phys.Soc.Jpn.62。