Optimal broadening of finite energy spectra in the numerical renormalization group: application to dissipative dynamics in two-level systems

TL;DR

This paper introduces an optimized frequency-dependent broadening technique in numerical renormalization group calculations, enabling high-precision analysis of dissipative dynamics in quantum impurity models, especially near sharp spectral features.

Contribution

It presents a novel method combining level bunching exploitation and frequency-dependent broadening to improve spectral resolution in NRG calculations.

Findings

Enhanced resolution of dissipative atomic peaks.

Accurate characterization of the crossover in the spin boson model.

Significant computational efficiency gains.

Abstract

Numerical renormalization group (NRG) calculations of quantum impurity models, based on a logarithmic discretization in energy of electronic or bosonic Hamiltonians, provide a powerful tool to describe physics involving widely separated energy scales, as typically encountered in nanostructures and strongly correlated materials. This main advantage of the NRG was however considered a drawback for resolving sharp spectral features at finite energy, such as dissipative atomic peaks. Surprisingly, we find a bunching of many-body levels in NRG spectra near dissipative resonances, and exploit this by combining the widely-used Oliveira's $z$-trick, using an averaging over {\it few} discrete NRG spectra, with an optimized {\it frequency-dependent} broadening parameter $b(\w)$. This strategy offers a tremendous gain in computational power and extracts all the needed information from the raw NRG data without {\it a priori} knowledge of the various energy scales at play. As an application we investigate with high precision the crossover from coherent to incoherent dynamics in the spin boson model.