Effects of phonon, orbital and disorder on the Mott transition

1.用动力学平均场理论研究了轨道简并Hubbard模型中Mott金属-绝缘体的相变。由于包含了Hund规则交换J，使得U_c的临界值大大降低。对于任意有限的J_2，从连续的J=0转变为不连续的。用数值对角化方法研究了一维多轨道Hubbard模型。由于Hund规则耦合和晶场分裂的竞争，全极化的铁磁性相对于部分极化的铁磁性变得不稳定。用数值对角化和重整化群相结合的方法研究了一维扩展Hubbard模型中金属-绝缘体相变附近的临界行为。4.研究了半填充Holstein-Hubbard模型中金属-绝缘体相变与局域电子-电子相互作用U和电子-声子耦合g的关系。当U占主导时，金属-绝缘体转变为Mott-绝缘体；当g占主导时，转变为局域双极化态。在前一种情况下，跃迁总是二阶的，而在后一种情况下，当u5较大时，它是一阶的。用动力学平均场理论研究了周期Anderson-Holstein模型。在强电声子耦合区，系统表现出反常的重费米子行为，并伴随着较大的晶格涨落和极端的声子软化。离子在弱耦合区的简谐势在强耦合区转变为有效的双势垒势。

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.