  We exploit the common mathematical structure of the numerical renormalization
group and the density matrix renormalization group, namely, matrix product
states, to implement an efficient numerical treatment of a two-lead,
multi-level Anderson impurity model. By adopting a star-like geometry, where
each species (spin and lead) of conduction electrons is described by its own
Wilson chain, instead of using a single Wilson chain for all species together,
we achieve a very significant reduction in the numerical resources required to
obtain reliable results. We illustrate the power of this approach by
calculating ground state properties of a four-level quantum dot coupled to two
leads. The success of this proof-of-principle calculation suggests that the
star geometry constitutes a promising strategy for future calculations the
ground state properties of multi-band, multi-level quantum impurity models.
Moreover, we show that it is possible to find an "optimal" chain basis,
obtained via a unitary transformation (acting only on the index distinguishing
different Wilson chains), in which degrees of freedom on different Wilson
chains become effectively decoupled from each other further out on the Wilson
chains. This basis turns out to also diagonalize the model's chain-to-chain
scattering matrix. We demonstrate this for a spinless two-lead model,
presenting DMRG-results for the mutual information between two sites located
far apart on different Wilson chains, and NRG results with respect to the
scattering matrix.
