Improved estimator for numerical renormalization group calculations of the self-energy

TL;DR

This paper introduces a new estimator for the self-energy in numerical renormalization group calculations, reducing artifacts and computational effort, especially beneficial for complex multiorbital systems.

Contribution

A novel self-energy estimator based on equations of motion that improves accuracy and efficiency in NRG calculations for quantum impurity models.

Findings

Reduces artifacts in the imaginary part of the self-energy.

Achieves convergence with fewer states and less computational effort.

Applicable to multiorbital and dynamical mean-field theory systems.

Abstract

We present a new estimator for the self-energy based on a combination of two equations of motion and discuss its benefits for numerical renormalization group (NRG) calculations. In challenging regimes, NRG results from the standard estimator, a ratio of two correlators, often suffer from artifacts: the imaginary part of the retarded self-energy is not properly normalized and, at low energies, overshoots to unphysical values and displays wiggles. We show that the new estimator resolves the artifacts in these properties as they can be determined directly from the imaginary parts of auxiliary correlators and do not involve real parts obtained by Kramers-Kronig transform. Furthermore, we find that the new estimator yields converged results with reduced numerical effort (for a lower number of kept states) and thus is highly valuable when applying NRG to multiorbital systems. Our analysis is targeted at NRG treatments of quantum impurity models, especially those arising within dynamical mean-field theory, but most results can be straightforwardly generalized to other impurity or cluster solvers.