Many-body Problems in Condensed Matter Physics

凝聚态物理中的多体问题

• 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

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.

在本项目期间，开始了对元胞RVB态自旋能隙相的国际合作，并已发展到对Neel有序相和元胞RVB相之间量子相变临界行为的研究。用量子环算法MonteCarlo模拟表明，临界指数与经典的O（3）指数一致，这支持了到非线性sigma模型的映射。本项目研究的另一个重要问题是二维金属-绝缘体相变。通过量子MonteCarlo模拟和标度理论，得到了超标度假设成立的结论，动力学指数为z= 4.对于重费米子，利用密度矩阵重整化群研究了一维Kondo晶格模型.在顺磁性金属相中，首次观察到自旋和电荷的Friedel振荡。从振荡周期可以看出，费米面很大，费米动量由传导电子密度和局域自旋决定.这种方法使我们能够确定石墨、硅化物、BC_2N等的结构转变的过渡态。

项目成果

H.Tsunetsugu: "Rigorous Results for Half-Filled Kondo Lattices" Phys.Rev.B. 55. 3042-3045 (1997)

H.Tsunetsugu：“半填充近藤晶格的严格结果”Phys.Rev.B。

N.Shibata: "Neel Orders,Haldane Gap and Kondo Singlet Phase in the Anisotropic Kondo Chain" Physical Review B. 51. 3626-3631 (1995)

N.Shibata：“各向异性近藤链中的 Neel Orders、Haldane Gap 和 Kondo Singlet Phase”物理评论 B. 51. 3626-3631 (1995)

M.Troyer: "Nearly Critical Ground State of LaCuO_<2.5>" Phys.Rev.B (in press).

M.Troyer：“LaCuO_<2.5> 的近临界基态”Phys.Rev.B（正在出版）。

Y.Tateyama: "Ab Initio Study on the Transformation Path under Pressure between Graphite and Diamond" (発表予定).

Y.Tateyama：“从头开始研究石墨和金刚石之间压力下的转变路径”（待提交）。

K.Ueda: "Plaquette Resonating-Valence-Bond Ground State of CaV_4O_9" Phys.Rev.Lett.76. 1932-1935 (1996)

K.Ueda：“CaV_4O_9 的板共振价键基态”Phys.Rev.Lett.76。