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

• Applicant: Professor Dr. Christoph Karrasch
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 271732007

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.

• DFG Programme: Independent Junior Research Groups