## Research topics

I conduct research in condensed matter theory. My research interests include the following topics.

### Low-dimensional materials

My goal is a better theoretical understanding of condensed matter physics in reduced dimensions. The focus lies on the Peierls transition, Luttinger liquids, and the dimensional crossover in strongly anisotropic (quasi-one-dimensional) solids as well as in atomic quantum wires on surfaces. The main question is the role of the weak but not negligible three-dimensional couplings between the quasi-one-dimensional components in theses materials.

### Physics of strongly correlated electrons

Understanding the role of strong electronic correlations in a central question of condensed matter physics. I study phenomena such as the Mott metal-insulator transition, Luttinger liquids, superconductivity, charge density waves, and polarons in basic lattice models of solid-state physics such as the Hubbard model for interacting electrons or the Holstein model for coupled electrons and lattice vibrations (phonons). The main methods are matrix-product-state algorithms such as the density-matrix renormalization group and the time-evolving block decimation.

### Quantum many-body theory

In the theory of quantum many-body systems there is a great need for better theoretical tools. Thus the developement of new methods for these systems is one of my main goals. The focus lies on numerical matrix-product-state methods since several years. Moreover, I explore other approches based on reduced density matrices.