Faculty of Physics
Tel. +49 89 2180 4527
Research focus: computational methods, condensed-matter, quantum many-body physics
Correlated open quantum systems
Research in our group focusses on open correlated quantum systems. The combination of "open" and "correlated" leads to many fascinating phenomena in experiment, and poses interesting methodological challenges for theoretical work. We are particularly interested in electron transport in interacting mesoscopic and nanoscale systems, such as quantum dots, quantum wires, quantum point contacts and disordered conductors, and in the driven dynamics of local degrees of freedom coupled to a dissipative bath, such as an exciton tunnel-coupled to an electron gas.
Since experimentally relevant models are very often too complicated to admit a full analytical treatment, much of our work has a significant numerical component. The two approaches that we currently rely on most are the functional renormalization group (fRG), and numerical tensor network methods methods for treating quantum impurity models.
fRG is in essence an RG-enhanced way of doing perturbation theory in the interaction. We have recently developed a version of this approach suitable for studying (not-too-strongly) interacting open quantum systems that lack translational symmetry. We have used it to develop a microscopic understanding of the 0.7-anomaly in quantum point contacts, and are currently extending our treatment of this system to include various types of complications, such as spin-orbit interactions or superconducting correlations, and nonequilibrium transport using Keldysh-fRG.
Tensor networks and quantum impurity models
Our interest in tensor networks has evolved in the context of quantum impurity models, which describe discrete quantum degrees of freedom coupled to a bath of excitations. The most powerful numerical method for treating such systems has for many years been the numerical renormalization group (NRG). We realized about 10 years ago that this method has the same mathematical basis as the density matrix renormalization group (DMRG) for solving 1-dimensional quantum chain models, in that both employ matrix product states (MPS), a one-dimensional example of a tensor network.
My coworker Anreas Weichselbaum has exploited this fact to develop a uniquely flexible and optimized 1d-tensor network code that combines advantages of both methods and exploits non-Abelian symmetries, resulting in a very powerful and versatile tool for treating interacting low-dimensional quantum systems. We are currently working to implement non-Abelian symmetries also in codes for two-dimensional tensor networks.