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We introduce a block Lanczos (BL) recursive technique to constructquasi-one-dimensional models, suitable for density-matrix renormalization group(DMRG) calculations, from single- as well as multiple-impurity Anderson modelsin any spatial dimensions. This new scheme, named BL-DMRG method, allows us tocalculate not only local but also spatially dependent static and dynamicalquantities of the ground state for general Anderson impurity models withoutlosing elaborate geometrical information of the lattice. We show that theBL-DMRG method can be easily extended to treat a multi-orbital Andersonimpurity model. We also show that the symmetry adapted BL bases can beutilized, when it is appropriate, to reduce the computational cost. As ademonstration, we apply the BL-DMRG method to three different models forgraphene: (i) a single adatom on the honeycomb lattice, (ii) a substitutionalimpurity in the honeycomb lattice, and (iii) an effective model for a singlecarbon vacancy in graphene. Our analysis reveals that, for the particle-holesymmetric case at half filling of electron density, the ground state of model(i) behaves as an isolated magnetic impurity with no Kondo screening while theground state of the other two models forms a spin singlet state. We alsocalculate the real-space dependence of the spin-spin correlation functionsbetween the impurity site and the conduction sites for these three models. Ourresults clearly show that, reflecting the presence of absence of unscreenedmagnetic moment at the impurity site, the spin-spin correlation functions decayas $r^{-3}$, differently from the non-interacting limit ($r^{-2}$), for model(i) and as $ r^{-4}$, exactly the same as the non-interacting limit, for models(ii) and (iii) in the asymptotic $r$, where $r$ is the distance between theimpurity site and the conduction site.

physical review. b, condensed matter and materials physics

Block Lanczos density-matrix renormalization group method for general  Anderson impurity models: Application to magnetic impurity problems in  graphene