Energy resolution and discretization artefacts in the numerical renormalization group

Abstract

We study the limits of the energy resolution that can be achieved in the calculations of spectral functions of quantum impurity models using the numerical renormalization group (NRG) technique with interleaving (z-averaging). We show that overbroadening errors can be largely eliminated, that higher-moment spectral sum rules are satisfied to a good accuracy, and that positions, heights and widths of spectral features are well reproduced; the NRG approximates very well the spectral-weight distribution. We find, however, that the discretization of the conduction-band continuum nevertheless introduces artefacts. We present a new discretization scheme which removes the band-edge discretization artefacts of the conventional approach and significantly improves the convergence to the continuum (Lambda -> 1) limit. Sample calculations of spectral functions with high energy resolution are presented. We follow in detail the emergence of the Kondo resonance in the Anderson impurity model as the electron-electron repulsion is increased, and the emergence of the phononic side peaks and the transition from the spin Kondo effect to the charge Kondo effect in the Anderson-Holstein impurity model as the electron-phonon coupling is increased. We also compute the spectral function of the Hubbard model within the dynamical mean-field theory (DMFT), confirming the presence of fine structure in the Hubbard bands.

17 pages, 19 figures

References in corpus (7)

• The numerical renormalization group method for quantum impurity systems
• Many Body Effects on the Transport Properties of Single-Molecule Devices
• Quantum transport through a deformable molecular transistor
• Electron spectra close to a metal-to-insulator transition
• Universal dephasing rate due to diluted Kondo impurities
• Spectral Densities from Dynamic Density-Matrix Renormalization
• Spin-charge separation and simultaneous spin and charge Kondo effect

Cited by in corpus (4)

• Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces
• Adaptive logarithmic discretization for numerical renormalization group methods
• Generic susceptibilities of the half-filled Hubbard model in infinite dimensions
• NRG calculations of the ground-state energy: application to the correlation effects in the adsorption of magnetic impurities on metal surfaces