Effects of phonon, orbital and disorder on the Mott transition

1.利用动力学平均场理论研究了轨道简并Hubbard模型中的Mott金属-绝缘子跃迁。包含Hund的规则交换J会导致临界值U_c的大幅降低。对于任意有限的J.2，这种转变从定性上从J=0的连续转变为不连续。采用数值对角化方法研究了一维多轨道Hubbard模型。由于洪德规则耦合和晶体场分裂的竞争，完全极化铁磁性相对于部分极化铁磁性变得不稳定。在部分极化铁磁附近观察到超导相。采用数值对角化和重整化群相结合的方法，研究了四分之一填充时具有现场相互作用和最近邻相互作用的一维扩展Hubbard模型在金属-绝缘子过渡附近的临界行为。研究了半填充Holstein-Hubbard模型中金属-绝缘体跃迁与电子-电子相互作用U和电子-声子耦合g的关系。当U占主导时，跃迁向mott -绝缘体；当g占主导时，跃迁到局域双极态。在前一种情况下，过渡总是二阶的，而在后一种情况下，当u值较大时，它变成一阶的。利用动力学平均场理论研究了周期Anderson-Holstein模型。在强电子-声子耦合状态下，系统表现出反常的重费米子行为，伴随着较大的晶格涨落和极端的声子软化。弱耦合状态下离子的简谐波势在强耦合状态下转变为有效的双阱势。

1.The Mott metal-insulator transition in the orbitally degenerate Hubbard model is studied by means of the dynamical mean-field theory. Inclusion of the Hund's rule exchange J results in a strong reduction of the critical value U_c. The transition turns out to change qualitatively from continuous for J=0 to discontinuous for any finite J.2.The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the competition between Hund's rule coupling and crystal-field splitting, the fully polarized ferromagnetism becomes unstable against the partially polarized one. The superconducting phase is observed in the vicinity of the partially polarized ferromagnetism.3.The critical behavior near the metal-insulator transition in the one-dimensional extended Hubbard model with the on-site and the nearest-neighbor interactions at quarter filling is studied using a combined method of the numerical diagonalization and the renormalization group.4.The metal-insulator transitions in the half-filled Holstein-Hubbard model is investigated as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. When U is dominant the transition is to a Mott-insulator ; when g dominates, the transition is to a localized bipolaronic state. In the former case, the transition is always found to be second order, while, in the latter case, it becomes first order for larger values of U.5.The periodic Anderson-Holstein model is studied by using the dynamical mean-field theory. In the strong electron-phonon coupling regime, the system shows an anomalous heavy-fermion behavior which is accompanied by a large lattice fluctuation and an extreme phonon softening. A simple harmonic potential for ions in the weak coupling regime changes into an effective double-well potential in the strong coupling regime.