# Research & Funding

Learn more about our research and funding.

Our research in the field of theoretical condensed matter physics is crucially driven by the plethora of emergent collective phenomena that arise in many-body systems and by its connections to and relevance for data, material, and quantum information science.

We work on a broad variety of realizations of many-body physics, ranging from engineered heterostructures and moiré superlattice systems, topological semi-metals, high-temperature superconductors, frustrated magnets, to ultra-cold atomic systems and exotic toy models, such as fracton models. The ultimate goal of our work is to understand the complex behavior of novel many-body systems in terms of effective theories, that are guided by symmetry- and topology-based arguments, energetics, and experiment. To this end, we employ a combination of analytical and numerical methods of quantum field theory and statistical mechanics, more recently also machine-learning techniques, and enjoy close collaborations with experimental groups.

More specifically, we are interested in the following sets of problems and questions:

### Unconventional superconductivity

i.e., superconductivity beyond the BCS paradigm. How can we determine the microscopic form of the superconducting order parameter, in particular, its **symmetry and topological properties**? What are the key degrees of freedom hosting superconductivity that need to be included in a minimal model for it? What is the impact of different types of **impurities** on superconductivity? Is **spin-orbit coupling** relevant? What are competing phases? One of the long-term goals is to design and control material realizations of exotic superconducting phases, such as topological superconductivity, which could be used, e.g., for **quantum computation** applications.

### Quantum spin liquids

which are phases of frustrated quantum magnets characterized by **topological order** rather than broken symmetries. How can these, so far, elusive states of matter be identified experimentally? Motivated by their potential relevance to the cuprate **high-temperature superconductors** and **twisted multilayer graphene**, we work on models where spin liquids can coexist with metallic phases and the underlying topological order is intertwined with broken symmetries. What are the characteristic spectral and **transport** features? We are interested in the detailed comparison between predictions of candidate effective field theories and both numerical studies of the **Hubbard model** and experiment.

### Interaction effects in & stability of topological phases

How can topological phases arise spontaneously as a consequence of interactions? Can **disorder** stabilize non-trivial topological states? What is the interplay of **topological obstructions** and strong interactions? Are topological terms, such as **Wess-Zumino-Witten terms**, relevant to the phase diagram of twisted-bilayer graphene? What is the impact of phase competition on a topological phase and on its signatures? How fragile are topological qubits against **time-dependent **or** non-Hermitian perturbations**?

### Machine learning for many-body physics

as a useful complementary tool to solve difficult physics problems. We have a particular interest in unsupervised algorithms that can learn directly from the data and do not require human supervision. We apply machine learning techniques both to **numerically generated** and **experimental data**, e.g., to classify phases and to learn something about the microscopic physics from experiment, respectively. This line of research is also motivated by the hope of **mutual benefits** in the sense that concepts and formalisms of theoretical physics might prove useful to understand how machine-learning techniques work and vice versa.