Comparison of the 1/N expansion and Bethe ansatz results for the degenerate Anderson model

Rasul, J.W.; Hewson, A. C.

doi:10.1088/0022-3719/17/19/010

Cited by 52 publications

(19 citation statements)

References 17 publications

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“…Such differences can occur in calculations where the high energy excitations, or high cut-offs, are treated differently. This situation occurs for the N -fold degenerate models (U = ∞) where the imposition of the high energy cut-off D ′ in the Bethe ansatz calculations for the linear dispersion model differs from the band width D for the conventional model, but a relation between these cut-offs can be found such that the results from the Bethe ansatz calculations can be translated into those for the conventional model [15]. A similar situation applies here.…”

Section: Results For Symmetric Modelmentioning

confidence: 71%

“…Once the renormalized parametersǫ d andṼ have been determined the free quasiparticle Hamiltonian can be diagonalized and written in the form (15) where p † k,σ , p k,σ , and h † k,σ , h k,σ , are the creation and annihilation operators for the quasiparticle and quasihole excitations, and Λ −(N −1)/2 E p,k (N ) and Λ −(N −1)/2 E h,k (N ) are the corresponding excitation energies relative to the ground or vacuum state |0 ; the scale factor Λ −(N −1)/2 is due to the fact that the energies are calculated for the rescaled Hamiltonian, which is such that E p,k (N ) and E h,k (N ) for k = 1 are of order 1. For the lowest-lying level particle and hole levels, we have E p (N ) = E p,1 (N ) and E h (N ) = E h,1 (N ).…”

Section: Calculation Of Renormalized Parametersmentioning

confidence: 99%

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Renormalized parameters for impurity models

2004

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Abstract. We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective levelǫ d , an effective hybridizatioñ V , and a quasiparticle interactionŨ . The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a FalikovKimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a FalikovKimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.PACS. 71.10.-w Theories and models of many-electron systems -71.27.+a Strongly correlated electron systems; heavy fermions -75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions

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Section: Results For Symmetric Modelmentioning

confidence: 71%

Section: Calculation Of Renormalized Parametersmentioning

confidence: 99%

Renormalized parameters for impurity models

2004

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“…Now, the influence of the background is strikingly illustrated by solving for the Kondo temperature only to the first order in 1/N f . 19 This causes indeed a substantial decrease, bringing the result close to the exact value. The correct doping dependence displays the upward curvature, as also seen in our approximations CFM1 and CFM2.…”

Section: Discussion and Outlookmentioning

confidence: 71%

“…: lowering of Z and upward curvature at the approach of zero doping (1 − n → 0), is close to that of the exact Kondo scale in the Bethe ansatz solution for the Anderson impurity. 19 …”

Section: Improving the Dynamical Weight Transfermentioning

confidence: 99%

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Spectral density of the Hubbard model by the continued fraction method

2006

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We present the continued fraction method (CFM) as a new microscopic approximation to the spectral density of the Hubbard model in the correlated metal phase away from half filling. The quantity expanded as a continued fraction is the single particle Green function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. The new aspect is to add further stages to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green function on equal footing and determine the energy scale of the Fermi liquid quasiparticles by minimizing the total energy. The solution is free of phenomenological parameters and remains well defined in the strong coupling limit, near the doping controlled metal-insulator transition. Our results for the density of states agree reasonably with several variants of the dynamical mean field theory. The CFM requires minimal numerical effort and can be generalized in several ways that are interesting for applications to real materials.

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Theory of correlated holes (and electrons): From satellites to Luttinger liquids

Zaanen¹

1992

Topics in Applied Physics

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Comparison of the 1/N expansion and Bethe ansatz results for the degenerate Anderson model

Cited by 52 publications

References 17 publications

Renormalized parameters for impurity models

Renormalized parameters for impurity models

Spectral density of the Hubbard model by the continued fraction method

Theory of correlated holes (and electrons): From satellites to Luttinger liquids

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