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

TL;DR

This study uses the density matrix renormalization group method to analyze the ground state phase diagram of the single impurity Anderson model on a honeycomb lattice, identifying two phases and demonstrating the utility of entanglement spectra in phase boundary detection.

Contribution

It provides the first quantitative comparison between the honeycomb lattice Anderson model and a pseudogap model, validating low-energy approaches and highlighting entanglement spectrum as a phase transition indicator.

Findings

Identification of local moment and asymmetric strong coupling phases.

Agreement between honeycomb lattice and pseudogap Anderson models at low energies.

Entanglement spectrum degeneracies characterize phase boundaries.

Abstract

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.