The density-matrix renormalization group method (DMRG) has established itself over the
last decade as the leading method for the simulation of the statics and dynamics of one-
dimensional strongly correlated quantum lattice systems. In the further development of the
method, the realization that DMRG operates on a highly interesting class of quantum states,
so-called matrix product states (MPS), has allowed a much deeper understanding of the
inner structure of the DMRG method, its further potential and its limitations. In this paper, I …