Realistic calculations of electronic properties of transition metal oxides and quantum dots

用受控近似法计算真实的材料或器件的电子性质是现代固体物理理论的重要挑战之一。如果电子由于强库仑相互作用而强关联，则这项任务变得特别困难。在这个方向上的一个重大突破是最近发展的局域密度近似（LDA）和多体动力学平均场理论（DMFT）的密度泛函理论的合并，迄今已成功地应用于少数材料与弦电子关联。LDA+DMFT方法的进一步发展及其在过渡金属氧化物中的应用是第一个提出的项目。第二个项目是开发一种方法，用于真实描述具有不规则边界的量子点。在大电导率的普适极限下，量子点的单粒子态以及量子点与引线的耦合可以用随机矩阵理论（RMT）描述。考虑到量子点中的库仑排斥，得到了与DMFT方程自洽解相同的多带安德森杂质模型。采用量子蒙特卡罗模拟方法分析RMT分布参数的安德森杂质模型。

The calculation of electronic properties of real materials or devices by controlled approximations is one of the most important challenges of modern theoretical solid state physics. This task becomes particularly difficult if the electrons are strongly correlated due to a strong Coulomb interaction. A major breakthrough in this direction was the recently developed merger of density functional theory in the local density approximation (LDA) and many-body dynamical mean field theory (DMFT) which has been successfully applied so far to a few materials with string electronic correlations. The further development of this LDA+DMFT method and its application to transition metaloxides is the first proposed project. The second project is to develop a method for the realistic description of quantum dots with irregular boundaries. In the universal limit of a large Thouless conductance, the one-particle states of these quantum dots and the coupling to the leads can be described by random matrix theory (RMT). Taking into account the Coulomb repulsion in the quantum dot results in the same kind of multi-band Anderson impurity model as that arising in the self-consistent solution of the DMFT equations. The Anderson impurity model with RMT distributed parameters shall be analyzed by means of quantum Monte Carlo simulations.