Solving dynamical mean-field theory using matrix product states
This thesis advances and applies matrix product state (MPS) based algorithms to the solution of dynamical mean-field theory (DMFT) and its variants. The advances enable to solve quantum many-body problems in and out of equilibrium that were previously out of reach for any\nnumerical treatment. In equilibrium, this concerns in particular the computation of the electronic --- such as insulating, metallic,\nspin-freezed and many other --- phases of highly complex realistic models for correlated materials. In non-equilibrium, this concerns in\nparticular the understanding of the fundamental mechanisms of the relaxation behavior of quantum many-body systems on short and intermediate time scales.