Correlation effects in one- and two-dimensional electron systems in and out of equilibrium

低维电子系统控制着强各向异性材料（如铁磷属元素化物）、石墨烯或量子点和量子线的行为。1D或2D费米子或玻色子也可以在冷原子装置中实现，其中可以精确地探测基本平衡或真实的时间物理。因此，了解低维系统是很重要的基础和应用在纳米电子学或功能材料的设计。然而，库仑相互作用导致的各种多体现象，不能得到使用简单的微扰理论。特别具有挑战性的是处理热平衡的系统。我的研究项目的目标是双重的：a）我想开发新的方法，可以描述实时，非平衡动力学的相关效应。B）我想用这些方法以及各种现有的方法来研究相互作用的一维和二维系统的许多性质。我的特别目标是同时从互补的角度来处理一个给定的问题，通过使用不同的半解析以及计算技术，每一个都有自己的优势和局限性。一个项目是计算线性响应动态相关函数的一维系统，如动量和频率分辨的态密度（可以使用光电发射测量）或光学电荷，自旋和热导率。特别是，a）我将试图证实最近的一个关于偏离传统低能“Luttinger液体”理论的基本猜想，B）我想解决与实际实验设置相关的模型（例如，扩展的哈伯德模型）在有限温度下，c）我将研究真正的长程相互作用。第二个项目是开发和实现技术，用它可以模拟二维相关系统的非平衡时间演化。这在很大程度上是未知领域，因此我将首先探索各个方法的功能。此后，我将研究原型问题：基本激发如何传播？非平衡态中是否存在可以在冷原子实验中测试的相互作用效应？我们能计算扩散常数吗？热力学量（虚时间演化）是否提供了关于不同有序相的见解？实时动力学可以用来计算二维相关函数吗？我的第三个目标是研究1d和2d系统中相互作用和无序的相互作用。这个问题的“多体版本”的安德森本地化是新出现的。我将尝试计算实验上可获得的特征的金属和绝缘阶段，以及性质的“动态量子相变”，其中分离他们，这应该是根本上不同于传统的安德森金属绝缘体transition.In合作，我的同事在FU柏林，我将研究的影响，相关性的拓扑系统。

Low-dimensional electron systems govern the behavior of strongly anisotropic materials (such as the iron pnictides), of graphene, or of quantum dots and wires. 1d or 2d fermions or bosons can also be realized in cold atom setups where elementary equilibrium or real time physics can be probed accurately. Thus, understanding low-dimensional systems is important both fundamentally and for applications in nanoelectronics or the design of functional materials. However, Coulomb interactions lead to a variety of many-body phenomena that cannot be obtained by using simple perturbation theory. It is particularly challenging to treat systems out of thermal equilibrium. The goal of my research project is two-fold: a) I want to develop novel methods with which one can describe correlation effects on real-time, non-equilibrium dynamics. b) I want to use these methods as well as a variety of existing ones to study numerous properties of interacting 1d and 2d systems. My particular aim is to approach a given problem simultaneously from complementary angles by using different semi-analytical as well as computational techniques which each have their own strengths and limitations.One project is to calculate linear-response dynamic correlation functions of 1d systems such as the momentum- and frequency-resolved density of states (which can be measured using photoemission) or optical charge, spin, and heat conductivities. In particular, a) I will try to confirm a recent, fundamental conjecture about deviations from the conventional low-energy 'Luttinger liquid' theory, b) I want to address models relevant for actual experimental setups (e.g., the extended Hubbard model) at finite temperature, c) I will study true long-range interactions.A second project is to develop and implement techniques with which one can simulate the out-of-equilibrium time evolution of correlated systems in 2d. This is largely uncharted territory, so I will first explore the capabilities of the individual methods. Thereafter, I will study prototypical questions: How do elementary excitations propagate? Are there interaction effects in non-equilibrium that can be tested in a cold atom experiment? Can we compute diffusion constants? Do thermodynamic quantities (imaginary time evolution) provide insights about different ordered phases? Can real-time dynamics be used to compute correlation functions in 2d?My third goal is to investigate the interplay of interactions and disorder in 1d and 2d systems. This issue of a 'many-body version' of Anderson localization is newly emerging. I will try to compute experimentally-accessible features of the metallic and insulating phases as well as properties of the 'dynamical quantum phase transition' which separates them and which supposedly differs fundamentally from the conventional Anderson metal-insulator transition.In collaboration with my colleagues at the FU Berlin, I will study the effects of correlations in topological systems.