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Bulletin of the American Physical Society

The numerical renormalization group and multi-orbital impurity models

Andreas Weichselbaum, K. M. Stadler, Jan von Delft, Zhiping Yin, Gabriel Kotliar, Andrew K. Mitchell

Published Mar 16, 2016• 0 citations
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One of the most important and accurate approaches for studying interacting many-electron correlated systems is the quantum renormalization group (RG) procedure, upon which we propose a concept in the framework of natural orbitals so that we can generalize the RG into general orbital space. To demonstrate its effectiveness, we apply this new approach on a quantum cluster-impurity model with four impurities in comparison with the exact diagonalization method. We also find a shortcut to dramatically improving this RG procedure. A profound impact on the cluster dynamical mean-field theory and multi-impurity/orbital Kondo problems is further discussed.
We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green's functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.