Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

Karlsson, Daniel; Leeuwen, Robert van

doi:10.1103/physrevb.94.125124

Cited by 17 publications

(15 citation statements)

References 69 publications

(179 reference statements)

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“…Let us now examine analytical properties of the determinant of the single-particle Green's function, already analyzed to a certain extent in Refs. [5], [24] and [26]. Here, we shall show that the determinant of the single-particle Green's function can be expressed as a simple rational polynomial function as in Eq.…”

Section: Determinant Of Single-particle Green's Functionmentioning

confidence: 91%

Topological interpretation of the Luttinger theorem

Seki

Yunoki

2017

Phys. Rev. B

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Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for non metallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a non-perturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that the fundamental hypothesis of the Landau's Fermi-liquid theory, the number of fermions being equal to that of quasiparticles, is guaranteed if the Luttinger theorem is valid since the theorem states that the number of fermions is equal to the Luttinger volume. All these general statements are made possible because of the finding that the Luttinger volume is expressed as the winding number of the single-particle Green's function at finite temperatures, for which the complex analysis can be readily exploited.

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Section: Determinant Of Single-particle Green's Functionmentioning

confidence: 91%

Topological interpretation of the Luttinger theorem

Seki

Yunoki

2017

Phys. Rev. B

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“…Its straightforward inclusion, however, yields negative spectra in some frequency regions. This prohibits the usual probability interpretation and, even worse, it jeopardizes SC calculations since the resulting Green's function (GF) has the wrong analytic structure [53]. The key idea of the PSD scheme [51,52] consists in (1) writing a SE diagram as the sum of its partitions, i.e., diagrams with particle and hole propagators, (2) bisecting each partition into two half diagrams, (3) adding the missing half diagrams to form a perfect square, and (4) gluing the half diagrams back.…”

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confidence: 99%

Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals

et al. 2016

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We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on bulk sodium, appearance of the secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed.

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“…The zeroth-order approximations for the SEs c (1, 2) can be obtained by using the relations given by Eqs. (52) and (83). After the Hedin equations are solved, we calculate the nuclear SE, see for example Sec.…”

Section: Choice Of Reference Positionsmentioning

confidence: 99%

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

2020

Self Cite

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The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

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Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

Cited by 17 publications

References 69 publications

Topological interpretation of the Luttinger theorem

Topological interpretation of the Luttinger theorem

Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

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