XIV. The distribution of electrons round impurities in monovalent metals

Friedel, J.

doi:10.1080/14786440208561086

Cited by 1,031 publications

(289 citation statements)

References 31 publications

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“…Obviously, the minimum can well be fitted by a parabola as long as the temperature does not become so low, that numerical deficiencies near ω = 0 become predominant. Also its position and height, as well as the quadratic coefficient may be compared to exact results for Fermi liquids [11,58], e.g. as a guideline for corrective measures when using these impurity solvers in lattice-calculations.…”

Section: Fermi-liquid Propertiesmentioning

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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Section: Fermi-liquid Propertiesmentioning

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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show abstract

“…It has been known from early 1950th that screened Coulomb potential has a long-range oscillatory tail cos(2k F r + φ 0 )/r 3 at large distances r (k F is Fermi momentum). These oscillations are often called Friedel oscillations [25]. Due to these oscillations, the screened Coulomb interaction gets over-screened at some distances and becomes attractive.…”

Section: Introductionmentioning

confidence: 99%

Superconductivity from repulsive interaction

Maiti¹,

Chubukov²

2014

Novel Superfluids

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Abstract. The BCS theory of superconductivity named electron-phonon interaction as a glue that overcomes Coulomb repulsion and binds fermions into pairs which then condense and super-conduct. We review recent and not so recent works aiming to understand whether a nominally repulsive Coulomb interaction can by itself give rise to a superconductivity. We first discuss a generic scenario of the pairing by electron-electron interaction, put forward by Kohn and Luttinger back in 1965, and then turn to modern studies of the electronic mechanism of superconductivity in the lattice models for the cuprates, the Fe-pnictides, and the doped graphene. We show that the pairing in all three classes of materials can be viewed as lattice version of Kohn-Luttinger physics, despite that the pairing symmetries are different. We discuss under what conditions the pairing occurs and rationalize the need to do parquet renormalization-group analysis. We also discuss the interplay between superconductivity and density-wave instabilities.

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“…Historically, sum rules have also played an important role in our understanding of strongly correlated systems. In the context of the Kondo effect for example, the Friedel sum rule [4,5,6]…”

Section: Introductionmentioning

confidence: 99%

Sum rules and Ward identities in the Kondo lattice

2005

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We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large N limit, we are able to explicitly write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a "large" Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.

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XIV. The distribution of electrons round impurities in monovalent metals

Cited by 1,031 publications

References 31 publications

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

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

Superconductivity from repulsive interaction

Sum rules and Ward identities in the Kondo lattice

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