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

Axel Freyn and Serge Florens
Phys. Rev. B 79, 121102(R) – Published 19 March 2009

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 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.

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  • Received 14 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.121102

©2009 American Physical Society

Authors & Affiliations

Axel Freyn and Serge Florens

  • Institut Néel, CNRS and Université Joseph Fourier, 25 avenue des Martyrs, BP 166, 38042 Grenoble, France

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Issue

Vol. 79, Iss. 12 — 15 March 2009

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