Ulrich Schollwöck - Disentangling strongly correlated Quantum Systems

Strongly correlated quantum systems, where more traditional methods of quantum many-body physics fail, have attracted enormous attention over the last decades but still provide formidable problems for our understanding: High-T_c 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 presentselected results from areas which in my view present particularly interesting challenges also in the future: non-equilibrium dynamics of correlated systems (here: ultracold atoms in lattices) and material properties of threedimensionaltransition metal oxides.