Lanczos transformation for quantum impurity problems in d -dimensional lattices: Application to graphene nanoribbons

We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. We introduce many-body interactions in the form of a Kondo or Anderson impurity and we solve the low-dimensional problem using the density matrix renormalization group. The technique is particularly suited to study systems that are inhomogeneous, and/or have a boundary. The resulting dimensional reduction translates into a reduction of the scaling of the entanglement entropy by a factor L super(d-1), where is the linear dimension of the original dimensional lattice. We also study the localized edge states in graphene nanoribbons by attaching a magnetic impurity to the edge or the center of the system. For armchair metallic nanoribbons we find a slow decay of the spin correlations as a consequence of the delocalized metallic states.