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The density matrix renormalization group method is applied to obtain theground state phase diagram of the single impurity Anderson model on thehoneycomb lattice at half filling. The calculation of local static quantitiesshows that the phase diagram contains two distinct phases, the local moment(LM) phase and the asymmetric strong coupling (ASC) phase. These results aresupported by the local spin and charge excitation spectra, which exhibitqualitatively different behavior in these two phases and also reveal theexistence of the valence fluctuating point at the phase boundary. Forcomparison, we also study the low-energy effective pseudogap Anderson model.Although the high-energy excitations are obviously different, we find that theground state phase diagram and the asymptotically low-energy excitations are ingood quantitative agreement with those for the single impurity Anderson modelon the honeycomb lattice, thus providing the first quantitative justificationfor the previous studies based on low-energy approximate approaches.Furthermore, we find that the lowest entanglement level is doubly degeneratefor the LM phase, whereas it is singlet for the ASC phase and is accidentallythree fold degenerate at the valence fluctuating point. Our results thereforeclearly demonstrate that the low-lying entanglement spectrum can be used todetermine with high accuracy the phase boundary of the impurity quantum phasetransition.

Density matrix renormalization group study in energy space for a single-impurity Anderson model and an impurity quantum phase transition