Anderson transition in interacting electron systems

本研究的主要目的是研究相互作用电子系统中无序诱导的金属-绝缘体跃迁。这道题确实很难，但仍有一些提示。在高磁场的二维电子系统中，相互作用的电子系统可以映射到具有随机变化磁通的系统。我们对这种随机通量系统进行了数值模拟。我们计划在未来的项目中研究通量波动不仅在空间上而且在时间上的情况。另一种可能的方法是尺度理论。为此，我们详细分析了非相互作用系统中的安德森跃迁，特别是边界条件效应和电导分布。即使在没有相互作用的情况下，二维安德森跃迁也很有趣。在存在自旋轨道相互作用的情况下，这一点特别有趣。我们精确地确定了该体系的临界指数，并研究了减相的影响。我们还利用遗传算法研究了经典的库仑间隙。用能级统计的方法研究了量子库仑玻璃。

The main objective of this research is to investigate the disorder induced metal-insulator transition in interacting electron systems. This problem is really difficult but there still are hints. In 2D electron systems in high magnetic fields, the interacting electron systems can be mapped to the systems with randomly varying magnetic fluxes. We have simulated this random flux systems numerically. We are planning to investigate the case where the fluctuations of fluxes are not only spatially but also temporally in the future project. Another possible approach is the scaling theory. For that purpose, we have analyzed in detail the Anderson transition in non-interacting systems, especially the boundary condition effect and the conductance distribution.The two dimensional Anderson transition is of interest even in the absence of interaction. That in the presence of spin-orbit interactions is especially interesting. We have determined the critical exponent of this system precisely, and investigated the effect of dephasing.We have also investigated the classical Coulomb gap using the genetic algorithm. The quantum Coulomb glass has also been investigated using the method of level statistics.