Theoretical Studies on Strongly Correlated Electron Systems

目前和未来几年凝聚态物理学中最有趣和最重要的问题或多或少都与对强关联系统电子态的理解有关。这些体系包括：1.高T_c铜氧化物；2.过渡金属氧化物；3.金刚烷系和吖系化合物中的重电子；4.有机导体；5.介观体系。最重要的是，在研究过程中，我们建立了“Mott绝缘体附近的非均相金属态”的明确概念，这一概念与文1和2中遇到的问题直接相关。这个概念将成为下个世纪基础科学和应用科学的主要范式，就像当前半导体技术中的能带理论和费米液体理论一样。每个子类的主要活动如下：1.高T_c铜氧化物在掺杂和温度平面上建立相图，特别是自旋能隙现象的起源。单粒子谱的分析和超导序参数对称性的识别。基于规范场的分析和双层效应的研究。过渡金属氧化物基于d=*自旋费米子系统的巨磁电阻分析。莫特转变单粒子谱权重分裂的可能性。标度关系的提出，以及两种可能的转变奇异行为。基于d=*Hubbard模型的数值重整化方法的分析。基于d=*Anderson模型的近藤绝缘子的重电子自旋和电荷激发谱。有机导体在pi-d混合导体中Mott相变和Peierls相变之间的本质相互作用。肮脏Tomonaga-Luttinger液体量子化电导的介观崩塌。

The most interesting and important problem in condensed matter physics at present and years to come will more or less be associated with the understanding of the electronic state in strongly correlated systems. Those include 1.high T_c copper oxides 2.transition metal oxides 3.heavy electrons in lantanides and actinides 4.organic conductors 5.mesoscopic systems.The present research project aims at the theoretical studies on electronic states of these strongly correlated systems. Above all, in the course of the studies, we have established a clear concept of the "ansmalous metaallic state near the Mott insulator" which is directly associated with the problems encountered in 1 and 2. This concept will be a main paradigm of the basic and applied sciences of the next century, just as the band theory and the Fermi liquid theory are in the present semiconductor technology.Main activities on each subcategory are as follows ;1. High T_c Copper OxidesThe establishment of the phase diagram on the plane of doping and temperature, especially of the origin of spin gap phenomenon. Analysis of the one-particle spectrum and the identification of the symmetry of the superconductivity order parameter. Analysis based on the gauge fields and studies on the bi-layr effects.2. Transition Metal OxidesAnalysis of the giant magnets-resistance base on the d=* spin fermion systems.3. Mott TransitionPossibility of splitting of the one-particle spectrum weight. Proposal of the scaling relation, and possible two types of singular behaviors toward the transition. Analysis based on the numerical renormalization method on d=* Hubbard model.4. Heavy ElectronsSpin and charge excitation spectra of Kondo insulators based on d=* Anderson model.5. Organic ConductorsEssential interplay between Mott transition and Peierls transition in pi-d mixed conductors.6. Mesoscopics Collapse of the quantized conductance in dirty Tomonaga-Luttinger liquide.