Numerical renormalization group method for quantum impurity systems

By R. Bulla, T. Costi, Thomas Pruschke. 2007

1,044 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/87867c14aa072770fd778dc1f6ce9f5d81e765d1

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Spin excitations and correlations in scanning tunneling spectroscopy (2015, methodology): “g that we reach the limit of the perturbative approach. The full description of a spin system in the strong coupling regime requires complex theoreticalmethods like numericalrenormalizationgrouptheory[103, 36, 104] which are beyond the scope of this paper. Nevertheless, we can discuss some of the ph”
Continuous-time Monte Carlo methods for quantum impurity models (2010, methodology): “There were too many states for exact diagonalization or NRG methods.”
Advances and challenges in single-molecule electron transport (2019, methodology): “For a detailed account of the general situation, we direct the reader to the original research articles and reviews (Bulla et al., 2008; Florens et al., 2011; Varma et al., 2002; Vojta, 2006).”
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, background): “It also fostered the development of new impurity solvers (Bulla et al., 2008; Gull et al., 2011b).”
Dynamics of non-Markovian open quantum systems (2015, methodology): “The numerical renormalization group (NRG) approach (Anders et al., 2007a; Bulla et al., 2008; Vojta et al., 2005), for instance, was initially derived in (Wilson, 1975) to analyze the problem of a quantum impurity coupled to a reservoir of noninteracting electrons (the Kondo problem).”
A substantial hybridization between correlated Ni-d orbital and itinerant electrons in infinite-layer nickelates (2019, background): “[49] Bulla, R.”