The main problem of quantum many-body physics is the fact that the Hilbert space grows exponentially with size. In other words if one considers a lattice, with some Hilbert space of dimension d on each site of the lattice, then the total Hilbert space would have dimension d N , where N is the number of sites on the lattice. For example, a spin-1/2 chain of length L has 2 degrees of freedom. The DMRG is an iterative, variational method that reduces effective degrees of freedom to those most important for a target state. The state one is most often interested in is the ground state.