Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution

Nozières, P.; Dominicis, C T de

doi:10.1103/physrev.178.1097

Cited by 1,505 publications

(928 citation statements)

References 7 publications

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“…The original problem 8,9 was formulated for conduction electrons with a small effective mass and valence electrons with a large effective mass, bombarded by x rays. The x rays knock one electron out of the valence band, leaving behind an essentially stationary hole.…”

Section: Fermi-edge Singularitymentioning

confidence: 99%

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Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer-Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green's functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering full counting statistics and the Fermi-edge singularity.

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Section: Fermi-edge Singularitymentioning

confidence: 99%

“…In the language of the original diagrammatic treatment of the FES problem, 8,9 it represents the total closed loop contribution. We may also write this closed loop contribution as…”

Section: Fermi-edge Singularitymentioning

confidence: 99%

Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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“…These are argued to contain those significant contributions, which are known to lead to the correct singular threshold behaviour of X-ray absorption spectra as predicted by Mahan [45] and calculated by Nozieres et al [16].…”

Section: Other Approximation Schemes In the Literaturementioning

confidence: 99%

Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems

Grewe¹,

Schmitt²,

Jabben³

et al. 2008

J. Phys.: Condens. Matter

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Abstract. For the treatment of interacting electrons in crystal lattices approximations based on the picture of effective sites, coupled in a self-consistent fashion, have proven very useful. Particularly in the presence of strong local correlations, a local approach to the problem, combining a powerful method for the short ranged interactions with the lattice propagation part of the dynamics, determines the quality of results to a large extent. For a considerable time the non crossing approximation (NCA) in direct perturbation theory, an approach originally developed by Keiter for the Anderson impurity model, built a standard for the description of the local dynamics of interacting electrons. In the last couple of years exact methods like the numerical renormalization group (NRG) as pioneered by Wilson, have surpassed this approximation as regarding the description of the low energy regime. We present an improved approximation level of direct perturbation theory for finite Coulomb repulsion U , the crossing approximation one (CA1) and discuss its connections with other generalizations of NCA. CA1 incorporates all processes up to fourth order in the hybridization strength V in a self-consistent skeleton expansion, retaining the full energy dependence of the vertex functions. We reconstruct the local approach to the lattice problem from the point of view of cumulant perturbation theory in a very general way and discuss the proper use of impurity solvers for this purpose. Their reliability can be tested in applications to e.g. the Hubbard model and the Anderson-lattice model. We point out shortcomings of existing impurity solvers and improvements gained with CA1 in this context. This paper is dedicated to the memory of Hellmut Keiter.

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“…Let us assume negligible V in the IRLM, but large value of |U f c |. Then we can utilize the analogy with the x-ray threshold problem 21 . Namely, neglecting the interference between U f c and V , the Coulomb interaction is replaced by the phase shift as…”

Section: B Vanishing Hybridization At Critical U F Cmentioning

confidence: 99%

“…Thus, α f = −δ/U f c for U f c > 0 and α f = 1 − δ/U f c for U f c < 0 in Eq. (21). The parameter α c is next determined from a condition for positive weight.…”

Section: B Monte Carlo Proceduresmentioning

confidence: 99%

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

2013

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The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction U f c and hybridization V . Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of U f c with a given value of V . For negative U f c , excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and U f c up to infinite order. As U f c becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.

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Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution

Cited by 1,505 publications

References 7 publications

Keldysh action of a multiterminal time-dependent scatterer

Keldysh action of a multiterminal time-dependent scatterer

Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

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