Abstract
Strongly correlated quantum systems, where more traditional methods of quantum manybody physics fail, have attracted enormous attention over the last decades but still provide formidable problems for our understanding:
high-Tc superconductors, frustrated quantum magnets, transition metal oxide and rear earth materials, ultracold atomic gases in optical lattices. Key numerical advances have been made using so-called tensor network methods, the best known of which is the density matrix renormalization group (DMRG).
After an introduction into the methodology, I want to present selected results from areas which in my view present particularly interesting challenges also in the future: nonequilibrium dynamics of correlated systems (here: ultracold atoms in lattices) and material properties of three-dimensional transition metal oxides.
