Single-particle dynamics of the Anderson model: a two-self-energy description within the numerical renormalization group approach

TL;DR

This paper compares the numerical renormalization group and local moment approach in analyzing the Anderson impurity model, demonstrating consistent results across different self-energy descriptions and energy scales.

Contribution

It introduces a two-self-energy description within NRG and shows its agreement with the LMA, providing a comprehensive understanding of single-particle dynamics.

Findings

Two-self-energy and single-self-energy descriptions yield the same spectrum.

NRG results agree well with analytical LMA results across energy scales.

Explicit NRG calculations of broken symmetry spectral components.

Abstract

Single-particle dynamics of the Anderson impurity model are studied using both the numerical renormalization group (NRG) method and the local moment approach (LMA). It is shown that a 'two-self-energy' description of dynamics inherent to the LMA, as well as a conventional 'single-self-energy' description, arise within NRG; each yielding correctly the same local single-particle spectrum. Explicit NRG results are obtained for the broken symmetry spectral constituents arising in a two-self-energy description, and the total spectrum. These are also compared to analytical results obtained from the LMA as implemented in practice. Very good agreement between the two is found, essentially on all relevant energy scales from the high-energy Hubbard satellites to the low-energy Kondo resonance.