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

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

2009-02-27

arxiv.org/abs/0902.4837v2

Phys. Rev. B (Rapid Communication) 79, 121102 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 5 figures. Minor modifications in V2

Scientific paper

10.1103/PhysRevB.79.121102

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.

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