Matrix product state comparison of the numerical renormalization group and the density matrix renormalization group

Wilson's numerical renormalization group (NRG) method for solving quantum impurity models can be turned into a variational method within the set of so-called matrix product states (MPS) with significantly more flexibility and efficient use of numerical resources. White's density matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPSs. 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 the DMRG approach. We explore to what extent NRG results can be improved upon systematically by performing a variational optimization in a space of variational matrix product states of the same structure as those used by NRG. We also compare the truncation schemes of NRG and DMRG, which are formulated in terms of energy eigenvalues or density matrix eigenvalues, respectively, and establish how many of the latter need to be kept to reproduce NRG eigenspectra using DMRG