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 numerical treatment. In equilibrium, this concerns in
particular the computation of the electronic --- such as
insulating, metallic, spin-freezed and many other --- phases of
highly complex realistic models for correlated materials. In
non-equilibrium, this concerns in particular the understanding of
the fundamental mechanisms of the relaxation behavior of quantum
many-body systems on short and intermediate time scales.