  Wilson's numerical renormalization group (NRG) method for solving quantum
impurity models yields a set of energy eigenstates that have the form of matrix
product states (MPS). White's density matrix renormalization group (DMRG) for
treating quantum lattice problems can likewise be reformulated in terms of MPS.
Thus, the latter constitute a common algebraic structure for both approaches.
We exploit this fact to compare the NRG approach for the single-impurity
Anderson model to a variational matrix product state approach (VMPS),
equivalent to single-site DMRG. For the latter, we use an ``unfolded'' Wilson
chain, which brings about a significant reduction in numerical costs compared
to those of NRG. We show that all NRG eigenstates (kept and discarded) can be
reproduced using VMPS, and compare the difference in truncation criteria, sharp
vs. smooth in energy space, of the two approaches. Finally, we demonstrate that
NRG results can be improved upon systematically by performing a variational
optimization in the space of variational matrix product states, using the
states produced by NRG as input.
