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

Abstract

We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single-as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multiorbital Anderson impurity model where not only inter-and intraorbital Coulomb interactions but also Hund's coupling and pair hopping interactions are included. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene with a structural defect and with a single hydrogen or fluorine absorbed, where a single Anderson impurity is coupled to conduction electrons in the honeycomb lattice. These models include (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis of the local dynamical magnetic susceptibility and the local density of states at the impurity site reveals that, for the particle-hole symmetric case at half-filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening, while the ground state of the other two models forms a spin-singlet state where the impurity moment is screened by the conduction electrons. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence or absence of unscreened magnetic moment at the impurity site, the spin-spin correlation functions decay as ∝ r −3 , differently from the noninteracting limit (∝ r −2 ), for model (i) and as ∝ r −4 , exactly the same as the noninteracting limit, for models (ii) and (iii) in the asymptotic r, where r is the distance between the impurity site and the conduction site. Finally, based on our results, we shed light on recent experiments on graphene where the formation of local magnetic moments as well as the Kondo-like behavior have been observed.

Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator

“…39 for an independent development of the same ideas). This approach enables one to study quantum impurity problems with a real space representation of the lattice, and in arbitrary dimensions, using the density matrix renormalization group method (DMRG) 40,41 .…”

Nonperturbative effects and indirect exchange interaction between quantum impurities on metallic (111) surfaces

“…In order to make the problem numerically tractable, we employ the so-called block Lanczos method recently introduced in this context by two of the authors 32,45 . This approach is inspired by Wilson's original formulation of the numerical renormalization group 46 , but accounting for the lattice structure.…”

Competition between Kondo effect and RKKY physics in graphene magnetism

“…We point out that this technique has been described in the literature in great detail 32,45 , so we cover only the essential aspects. Section III describes the exact results obtained with this approach both for single, and bi-layer graphene, illustrating the departure from conventional perturbative predictions.…”