My research in the field of theoretical condensed matter physics is crucially driven by the plethora of emergent collective phenomena that arise in manybody systems and by its connections to and relevance for data and quantum information science. I work on a broad variety of realizations of manybody physics, such as oxide heterostructures, moiré superlattice systems, topological semimetals, hightemperature superconductors, and ultracold atomic systems. The ultimate goal of my work is to understand the complex behavior of these systems in terms of effective theories, that are guided by symmetry and topologybased arguments, energetics, and experiment. To this end, I use a combination of both analytical and numerical methods of quantum field theory and statistical mechanics, more recently also machinelearning techniques, and enjoy direct collaborations with experimentalists and computational scientists.
More specifically, I am interested in the following sets of problems and questions:
Unconventional superconductivity. What can we learn about the microscopic form of the superconducting order parameter based on known properties of a material? What are its symmetry and topological properties? What is the impact of different types of impurities on superconductivity? Is spinorbit coupling relevant? What are the competing phases? I am particularly interested in superconductivity in systems with reduced symmetries as, e.g., very naturally arises at heterostructures, interfaces, and surfaces. One of the longterm goal is to design a material realization of a topological superconducting phase that can be used for quantum computations. 


Quantum spin liquids. How can these, so far, elusive states of matter be identified experimentally? Motivated by their potential relevance to the cuprate hightemperature superconductors and twisted multilayer graphene, I have been working on models where spin liquids can coexist with metallic phases and discussed how the underlying topological order can be intertwined with broken symmetries. What are the characteristic spectral and transport features? I am interested in the detailed comparison between predictions of candidate effective field theories and both numerical studies of the Hubbard model and experiment. How to describe the quantum critical point between the topologically ordered metallic phase and a Fermi liquid? Another related subject of interest is quantum chaos and its connection to thermalization and transport.

Interaction effects and stability of topological phases. How can topological phases arise spontaneously as a consequence of interactions in the system? Can disorder stabilize nontrivial topological states? Another set of questions concerns the stability of topological phases and qubits against perturbations: What is the impact of phase competition on a topological phase and on its signatures? How fragile is the "topological protection" against timedependent perturbations, e.g., those used to manipulate a topological qubit? 

Machine learning as a useful complementary tool to analyze difficult physics problems. In particular, I am interested in unsupervised algorithms that can learn directly from the data and do not require human supervision. Can we obtain insights about how a machinelearning algorithm works taking advantage of techniques developed in theoretical physics?
