Many-body Problems in Condensed Matter Physics

凝聚态物理中的多体问题

基本信息

批准号：
07044066
负责人：
UEDA Kazuo
金额：
$ 3.2万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for international Scientific Research
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07044066/
关键词：
condensed matter many-body problem strongly correlated electron system metal-insulator transition spin gap quantum Monte Carlo simulation density matrix renormalization group ab-initio calculations モット絶縁体重い電子系周期的アンダーソン模型 Car-Parrin

项目摘要

The international collaboration on the spin gap phase of the plaquette RVB state has started during the period of this project and has been evolved into the study on the critical behavior of the quantum phase transition between the Neel ordered phase and the plaquette RVB phase. By employing the quantum loop algorithm Monte Carlo simulations it is shown that the critical exponents agree with the classical O (3) exponents, which supports the mapping to the nonlinear sigma model.Another important problem studied in this project is the metal-insulator transition in two-dimension. By using quantum Monte Carlo simulations and the scaling theory, it is concluded that the hyperscaling hypothesis is valid in this case and the dynamical exponent is z=4.Concerning the heavy Fermions, the one-dimensional Kondo lattice model was investigated by using the density matrix renormalization group. In the paramagnetic metallic phase, spin and charge Friedel oscillations were observed for the first time. From the period of oscillations it is concluded that the Fermi surface is large in the sense that the Fermi momentum is determined by the sum of densities of conduction electrons and the localized spins.For the ab-initio calculations of electronic states, the constant pressure molecular dynamics method was developed. This method enables us to determine the transition states of structural transformations in graphite, silicides, BC_2N and others.

关于板状RVB态自旋间隙相的国际合作从本项目期间开始，并已发展为尼尔有序相与板状RVB相之间量子相变临界行为的研究。通过采用量子环算法蒙特卡罗模拟，结果表明临界指数与经典O(3)指数一致，支持映射到非线性sigma模型。本项目研究的另一个重要问题是金属-绝缘体转变。二维。通过量子蒙特卡罗模拟和标度理论，得出超标度假设在这种情况下是有效的，动力学指数为z=4。对于重费米子，利用密度研究了一维Kondo晶格模型矩阵重整化群。在顺磁金属相中，首次观察到自旋和电荷弗里德尔振荡。从振荡周期可以得出结论，费米面很大，因为费米动量是由传导电子和局域自旋的密度之和决定的。对于电子态的从头计算，恒压分子开发了动力学方法。该方法使我们能够确定石墨、硅化物、BC_2N 等结构转变的过渡态。