Development of a functional renormalization group to treat interaction effects in strongly disordered electron systems

相互作用和无序电子系统的分析处理采用微扰理论假设同时弱无序和弱相互作用。一般来说，这些方法在临界点附近，特别是在金属-绝缘体转变附近，电导率变得很小，无序不再被认为是弱的。因此，这样的方法不能给出明确的信息，在电子系统中的相互作用的影响或附近的本地化阈值。我们开始一个长期的活动，探索一种新的数值技术沿着线的功能重整化群。这种方法在相互作用中是微扰的，但在无序中（数值上）是精确的。我们的目标是研究相互作用对重要局域化跃迁的影响，包括整数量子霍尔跃迁和石墨烯材料中新预测的自组织跃迁。

Analytical treatments of interacting and disordered electron systems employ a perturbation theory assuming simultaneously weak disorder and weak interactions. Quite generally, these approaches break down near critical points, in particular near metal-insulator transitions, where the conductivity becomes small and the disorder no longer can be considered weak. Therefore, such methods cannot give unambiguous information about interaction effects in electron systems at or near the localization threshold. We start a longer term activity exploring a novel numerical technique along the lines of the functional renormalization group. The approach is perturbative in the interaction but (numerically) exact in the disorder. The goal is to study interaction effects on important localization transitions, including the integer quantum Hall transition and a newly predicted, self organized transition in the graphene material.