Correlated Fermions with Spin-Orbit Coupling and Competing Orders in Solids

固体中的相关电子表现出各种各样的迷人现象，从磁性和金属绝缘体转变到高温超导性。本项目旨在系统地研究凝聚态物理背景下相互作用费米子系统的相图。狄拉克材料，如石墨烯，以及越来越多的新型二维系统在存在足够强的相互作用时表现出多种可能的有序态。我们将探索有效的模型来分析这些顺序参数的竞争，并定量地确定它们在各种相变线相交处的临界行为。在许多新型材料和物质的拓扑状态中，有限自旋轨道耦合起着至关重要的作用。与此同时，电子-电子相互作用可以是相当大的，而相关效应和自旋轨道耦合之间的相互作用才刚刚开始被理解。我们将开发一种通用的方法来识别新兴的多体不稳定性，旨在对具有相当大的自旋轨道耦合的（二维）材料的低能特性进行无偏理论描述。该项目将采用重整化组的现代公式进行研究。

Correlated electrons in solids exhibit a huge variety of fascinating phenomena ranging from magnetism and metal-insulator transitions to high-temperature superconductivity. The project aims at systematically investigating the phase diagram of interacting fermion systems in the context of condensed matter physics. Dirac materials, such as graphene, and a growing number of novel two-dimensional systems exhibit a huge variety of possible ordered states in the presence sufficiently strong interactions. We shall explore effective models to analyze the competition of these order parameters and quantitatively determine their critical behaviour close to the intersection of various phase transition lines. In many novel materials and in topological states of matter, a finite spin-orbit coupling plays a crucial role. At the same time electron-electron interactions can be sizable and the interplay between correlation effects and spin-orbit coupling is only beginning to be understood. We will develop a versatile approach to identify emerging many-body instabilities aiming at an unbiased theoretical description of the low-energy properties of (two-dimensional) materials with sizable spin-orbit coupling. The project will be studied with modern formulations of the Renormalization Group.