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Theoretical Condensed Matter Physics

Research in Cologne

Research at the Institute for Theoretical Physics ranges from topological matter and quantum information science to quantum gravity and cosmology; from mathematical physics to research on novel materials. Close collaboration with experimental physicists, and colleagues from national and international partner institutions is an important aspect of our work. Our profile reflects in various collaborative research initiatives, such as the collaborative research center (CRC) on “Dynamics and Control of Quantum Materials” and the pan-European CRC “Entangled States of Matter” (with nodes in Copenhagen/Berlin/Cologne/Weizmann), which are pillars of the cluster of excellence “Matter and Light for Quantum Computing” (ML4Q) and the key profile areas “Quantum Matter and Materials” (QM2).

Research groups with close links to this master program include the one by Prof. Simon Trebst, which studies collective phenomena in quantum many-body systems that arise from the intricate interplay of topology, strong correlations, and spin-orbit coupling. In their work they typically complement analytical approaches by a variety of sophisticated numerical techniques that exploit concepts from statistical physics, quantum information theory, and computer science. The Cologne-Jülich group of Prof. Matteo Rizzi is working towards the theoretical understanding and experimental exploitation of many-body phenomena in “synthetic quantum matter”. To this end, the group develops and applies innovative control approaches as well as numerical simulation techniques such as tensor network algorithms. The group of Prof. Ralf Bulla is interested in exploring quantum impurity physics as a paradigm for a variety of physical systems, such as correlated fermions and bosons, and open quantum systems. A central theme is to establish links between different phenomena – such as Kondo physics, quantum dissipation, and Mott transitions – which can all be traced back to similar fundamental physical principles.

Contents within the Master Program

This focus area will provide an overview of modern numerical approaches to many-body systems, both classical and quantum. The in-depth introduction of elementary algorithms will include Monte Carlo methods, machine learning techniques, and entanglement based approaches (such as tensor networks), which will be complemented by an application of these methods to fundamental models and phenomena, mostly arising in the context of condensed matter physics, but one might branch out to other fields as well.

The fundamental physical principles of classical and quantum many-body systems will be taught in courses on advanced statistical physics & advanced quantum mechanics, which will be further expanded in our curriculum of quantum field theory lectures. Applications of these concepts in the context of material science will be presented in the course on solid state physics. Connections to classical field theory can be made in the lecture on hydrodynamics.

Participating Institutes

Institute for Theoretical Physics

Modules and Study Paths

Students will have to attend two compulsory modules, Advanced Quantum Mechanics and Computational Many-Body Physics. Together the two modules account for 15 CP. An additional 15 CP can be chosen from a set of modules:

Advanced Statistical Physics

Solid State Physics


Quantum Field Theory I

Quantum Field Theory II

A possible exemplary study plan could look like this:

Which topics in Mathematics/Computer Science suit this Area of Spezialization?

Suitable courses for Theoretical Condensed Matter Physics are Lectures from the areas of Applied Analytics, Algorithms and Numerical Mathematics and Scientific Computing.