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

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 few discrete NRG spectra, with an optimized frequency-dependent broadening parameter b(ω). This strategy offers a tremendous gain in computational power and extracts all the needed information from the raw NRG data without 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.