# Variational matrix-product-state approach to quantum impurity models Phys. Rev. B 80

Author(s): A. Weichselbaum, F. Verstraete, U. Schollwöck, J. I. Cirac, J. Delft

Journal: Phys. Rev. B

Volume: 80

Page(s): 165117

Year: 2009

DOI Number: 10.1103/PhysRevB.80.165117

We present a unified framework for 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 improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.