Adaptive broadening to improve spectral resolution in the numerical renormalization group

TL;DR

This paper introduces an adaptive broadening scheme for NRG spectral data that enhances resolution at finite energies by individually broadening contributions based on their sensitivity, outperforming conventional methods especially at coarser discretizations.

Contribution

The paper presents a novel adaptive broadening method for NRG that improves spectral resolution by tailoring broadening widths to each discrete contribution, reducing overbroadening of narrow features.

Findings

Better resolution of spectral features in non-interacting and interacting models.

More effective at coarser discretizations, reducing computational cost.

Minimizes artifacts in low-frequency linear broadening.

Abstract

We propose an adaptive scheme of broadening the discrete spectral data from numerical renormalization group (NRG) calculations to improve the resolution of dynamical properties at finite energies. While the conventional scheme overbroadens narrow features at large frequency by broadening discrete weights with constant width in log-frequency, our scheme broadens each discrete contribution individually based on its sensitivity to a z-shift in the logarithmic discretization intervals. We demonstrate that the adaptive broadening better resolves various features in non-interacting and interacting models at comparable computational cost. The resolution enhancement is more significant for coarser discretization as typically required in multi-band calculations. At low frequency below the energy scale of temperature, the discrete NRG data necessarily needs to be broadened on a linear scale. Here we provide a method that minimizes transition artefacts in between these broadening kernels.