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Numerical renormalization group method for quantum impurity systems

Ralf Bulla*, Theo A. Costi†, and Thomas Pruschke‡

Ralf Bulla*

  • Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany and Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany

Theo A. Costi†

  • Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany

Thomas Pruschke‡

  • Institut für Theoretische Physik, Universität Göttingen, 37077 Göttingen, Germany

  • *bulla@thp.uni-koeln.de
  • †t.costi@fz-juelich.de
  • ‡pruschke@theorie.physik.uni-goettingen.de
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Rev. Mod. Phys. 80, 395 – Published 2 April, 2008

DOI: https://doi.org/10.1103/RevModPhys.80.395

Abstract

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

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Rev. Mod. Phys. 80, 395– Published 2 April, 2008

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