  The density matrix renormalization group method is applied to obtain the
ground state phase diagram of the single impurity Anderson model on the
honeycomb lattice at half filling. The calculation of local static quantities
shows that the phase diagram contains two distinct phases, the local moment
(LM) phase and the asymmetric strong coupling (ASC) phase. These results are
supported by the local spin and charge excitation spectra, which exhibit
qualitatively different behavior in these two phases and also reveal the
existence of the valence fluctuating point at the phase boundary. For
comparison, we also study the low-energy effective pseudogap Anderson model.
Although the high-energy excitations are obviously different, we find that the
ground state phase diagram and the asymptotically low-energy excitations are in
good quantitative agreement with those for the single impurity Anderson model
on the honeycomb lattice, thus providing the first quantitative justification
for the previous studies based on low-energy approximate approaches.
Furthermore, we find that the lowest entanglement level is doubly degenerate
for the LM phase, whereas it is singlet for the ASC phase and is accidentally
three fold degenerate at the valence fluctuating point. Our results therefore
clearly demonstrate that the low-lying entanglement spectrum can be used to
determine with high accuracy the phase boundary of the impurity quantum phase
transition.
