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(如铁粒子)、石墨烯或量子点和量子线的行为。一维或二维费米子或玻色子也可以在冷原子装置中实现，在那里可以精确地探测基本平衡或实时物理。因此，了解低维系统在纳米电子学或功能材料设计中的基础和应用都是重要的。然而，库仑相互作用导致了各种各样的多体现象，这些现象是简单的微扰理论无法获得的。要使系统脱离热平衡，尤其具有挑战性。我的研究项目的目标有两个：a)我想开发新的方法，用来描述实时、非平衡动力学中的关联效应。B)我想使用这些方法以及现有的各种方法来研究相互作用的一维和二维系统的许多性质。我的特别目标是通过使用不同的半解析和计算技术从互补的角度同时处理给定的问题，这些技术都有各自的优势和限制。其中一个项目是计算一维系统的线性响应动态关联函数，例如动量和频率分辨的态密度(可以用光电发射测量)或光学电荷、自旋和热导。具体地说，a)我将尝试证实最近关于偏离传统低能Luttinger液体理论的一个基本猜想，b)我想解决与有限温度下的实际实验装置相关的模型(例如，扩展的Hubbard模型)，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人们可以用来模拟关联系统在2D中的非平衡时间演化的技术。这在很大程度上是未知的领域，因此我将首先探索各个方法的功能。然后，我将研究原型问题：基本激发是如何传播的？在非平衡状态下，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？热力学参数(假想的时间演化)是否提供了对不同有序相的洞察？实时动力学能用来计算二维的关联函数吗？我的第三个目标是研究一维和二维系统中相互作用和无序的相互作用。安德森本地化的多体版本的这一问题是新出现的。我将尝试计算金属相和绝缘相的实验可及特征，以及将它们分开的“动态量子相变”的性质，这种相变应该与传统的安德森金属-绝缘体相变有根本的不同。我将与我在柏林傅柏林的同事合作，研究拓扑系统中关联的影响。

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.