title: The density-matrix renormalization group: a short introduction.
abstract: The density-matrix renormalization group (DMRG) method 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. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.
authors.affiliation: Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, University of Munich, Theresienstrasse 37, 80333 Munich, Germany. schollwoeck@lmu.de
authors.forename: Ulrich
authors.initials: U
authors.lastname: Schollwöck