DMRG meets NRG

We present a unified framework of renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows to improve over Wilson's NRG for quantum impurity models by a variational method optimal in this framework. We illustrate it for the single-impurity Anderson model; moreover we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of off-resonance spectral properties, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting \emph{linear} scaling of complexity for $n$-channel problems.