Many-body Problems in Condensed Matter Physics

斑块RVB态自旋能隙相的国际合作始于本项目期间，并已发展到Neel有序相和斑块RVB相之间量子相变的临界行为的研究。通过使用量子环算法蒙特卡罗模拟表明，临界指数与经典的O(3)指数一致，支持到非线性Sigma模型的映射。本项目研究的另一个重要问题是金属-绝缘体的二维相变。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成立的，动力学指数为z=4。针对重费米子，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密度之和决定。对于电子态的从头计算，发展了恒压分子动力学方法。这种方法使我们能够确定石墨、硅化物、BC2N等的结构转变的过渡态。

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.