Scaling and the renormalization group in the kondo effect

Fowler, Michael; Zawadowski, A.

doi:10.1016/0038-1098(71)90324-3

Cited by 132 publications

(57 citation statements)

References 8 publications

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“…We start with the anisotropic generalization of the Kondo Hamiltonian, which is the proper starting model for a perturbative scaling analysis [21,100],…”

Section: Ferromagnetic Kondo Problem and The Anisotropic Kondo Problemmentioning

confidence: 99%

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Singular or non-Fermi liquids

2002

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“…We start with the anisotropic generalization of the Kondo Hamiltonian, which is the proper starting model for a perturbative scaling analysis [21,100],…”

Section: Ferromagnetic Kondo Problem and The Anisotropic Kondo Problemmentioning

confidence: 99%

“…Long before the solution of the Kondo problem, perturbative renormalization group for the effective vertex coupling constants J ± and J z as a function of temperature were obtained [21,100]. The scaling relation between them is found to be exact to all orders in the J s:…”

Section: Ferromagnetic Kondo Problem and The Anisotropic Kondo Problemmentioning

confidence: 99%

Singular or non-Fermi liquids

2002

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“…The fixed point of 2-loop calculation is an artifact arising from the third order approximation in J l lll 0 as in the singlechannel Kondo effect. 28,29) Detailed NRG studies show that the fixed point given by a 1-loop result might be realized. At the fixed point of the 1-loop calculation (and of course around the same energy region for the 2-loop one), dominant coupling constants are those between ðp þ ; s; p À Þ and ða 1 ; a 0 ; a À1 Þ, and become strong coupling.…”

Section: Two-dimensional Modelmentioning

confidence: 99%

Local Heavy Quasiparticle in Four-Level Kondo Model

2005

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An impurity four-level Kondo model, in which an ion is tunneling among 4-stable points and interacting with surrounding conduction electrons, is investigated using both perturbative and numerical renormalization group methods. The results of numerical renormalization group studies show that it is possible to construct the ground state wavefunction including the excited ion states if we take into account the interaction between the conduction electrons and the ion. The resultant effective mass of quasiparticles is moderately enhanced. This result offers a good explanation for the enhanced and magnetically robust Sommerfeld coefficient observed in SmOs 4 Sb 12 , some other filled-skutterudites, and clathrate compounds.

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“…For some of the quantum impurity models Bethe Ansatz, 3,4 conformal field theory, 5 bosonization, 6 perturbative calculations, 7,8 or a Fermi liquid theory 9 can provide a satisfactory explanation. However, these results are usually restricted to some regions in the parameter space.…”

Section: Introductionmentioning

confidence: 99%

Density matrix numerical renormalization group for non-Abelian symmetries

et al. 2008

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We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum impurity system. We illustrate the benefits of using non-Abelian symmetries by the example of calculations for the T -matrix of the two-channel Kondo model in the presence of magnetic field, for which conventional NRG methods produce large errors and/or take a long run-time.

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Scaling and the renormalization group in the kondo effect

Cited by 132 publications

References 8 publications

Singular or non-Fermi liquids

Singular or non-Fermi liquids

Local Heavy Quasiparticle in Four-Level Kondo Model

Density matrix numerical renormalization group for non-Abelian symmetries

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