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

通过控制近似计算实际材料或器件的电子特性是现代理论固体物理学最重要的挑战之一。如果电子由于强库仑相互作用而强相关，则这项任务变得特别困难。这方面的一个重大突破是最近发展起来的局部密度近似（LDA）中的密度泛函理论与多体动态平均场理论（DMFT）的合并，该理论迄今已成功地应用于一些具有弦电子相关的材料。第一个项目是进一步发展LDA+DMFT方法及其在过渡金属氧化物中的应用。第二个项目是开发一种具有不规则边界的量子点的现实描述方法。在大索氏电导的普遍极限下，这些量子点的单粒子态和与引线的耦合可以用随机矩阵理论（RMT）来描述。考虑了量子点的库仑斥力，得到了与DMFT方程自相容解相同的多带Anderson杂质模型。采用量子蒙特卡罗模拟的方法对具有RMT分布参数的Anderson杂质模型进行了分析。

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.