Abstract
Solving quantum problems with many strongly interacting electrons is one of the biggest and hardest problems in solid state physics. Even simplified models such as the Hubbard model remain very difficult to study, as the computation time and memory size generally increase exponentially with the size of the system. As a result, approximate numerical methods must be used to try and predict macroscopic properties. One of the approaches that has developed most over the last thirty years is the DMRG (density matrix renormalization group), which implements the ideas of renormalization by retaining at each stage only the most important states of the small systems that make up a large system. Ulrich Schollwöck's talk presented the main ideas behind this approach, and showed the link between DMRG and a variational method in the space of states that can be represented as matrix products.
