The numerical renormalization group method for quantum impurity systems
arXiv:cond-mat/0701105 · doi:10.1103/RevModPhys.80.395
Abstract
In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) 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 has been 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 of how to calculate 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.
55 pages, 27 figures, submitted to Rev. Mod. Phys
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- Antiferromagnetic Order of Strongly Interacting Fermions in a Trap: Real-Space Dynamical Mean-Field Analysis
- Friedel oscillations and the Kondo screening cloud
- Kondo proximity effect: How does a metal penetrate into a Mott insulator?
- Nonequilibrium isolated molecule limit
- Density matrix renormalization group approach of the spin-boson model
- Finite-temperature conductance signatures of quantum criticality in double quantum dots
- Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems
- Dissipative Two-Electron Transfer
- On the applicability of bosonization and the Anderson-Yuval methods at the strong-coupling limit of quantum impurity problems
- On a method to calculate conductance by means of the Wigner function: two critical tests