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Numerical renormalization group (NRG) calculations of quantum impuritymodels, based on a logarithmic discretization in energy of electronic orbosonic Hamiltonians, provide a powerful tool to describe physics involvingwidely separated energy scales, as typically encountered in nanostructures andstrongly correlated materials. This main advantage of the NRG was howeverconsidered a drawback for resolving sharp spectral features at finite energy,such as dissipative atomic peaks. Surprisingly, we find a bunching of many-bodylevels in NRG spectra near dissipative resonances, and exploit this bycombining the widely-used Oliveira's $z$-trick, using an averaging over {\itfew} discrete NRG spectra, with an optimized {\it frequency-dependent}broadening parameter $b(\w)$. This strategy offers a tremendous gain incomputational power and extracts all the needed information from the raw NRGdata without {\it a priori} knowledge of the various energy scales at play. Asan application we investigate with high precision the crossover from coherentto incoherent dynamics in the spin boson model.

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