Quantum Renormalization Groups Based on Natural Orbitals

We propose a new concept upon the renormalization group (RG) procedure for an interacting many-electron correlated system in the framework of natural orbitals, and formulate an algorithm for this RG approach. 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 algorithm. Further discussion is presented with the cluster dynamical mean-field theory and multi-impurity/orbital Kondo problems.