Momentum Distribution of an Interacting Electron Gas

Daniel, E.; Vosko, S. H.

doi:10.1103/physrev.120.2041

Cited by 193 publications

(89 citation statements)

References 6 publications

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“…(J3) can be reduced from ∞ to some finite multiple of k F ;σ without considerably affecting the behaviour of ̺ h σ ( r − r ′ ); in fact, as we shall see below, the behaviour of the first two leading terms in the AS of this function for r − r ′ → ∞ is fully determined by the behaviour of n σ (k) for k in some infinitesimal neighbourhood of k F ;σ , the Fermi wavenumber pertaining to fermions with spin index σ. We note that, in the paramagnetic phase, n(k) as calculated within the framework of the random-phase approximation (RPA) also decays like 1/k 8 as k → ∞ (Daniel and Vosko 1960). On the other hand, this decay is like 1/k 4 according to the calculations by Belyakov (1961).…”

Section: Sin(qr) (F34)mentioning

confidence: 89%

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Dynamical correlation functions expressed in terms of many-particle ground-state wavefunction; the dynamical self-energy operator

Farid

2002

Philosophical Magazine B

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We explicitly calculate the four leading-order terms of the formal asymptotic series for large |ε| (where ε denotes the external energy parameter) of the single-particle Green function Gσ(ε), σ ∈ {−s, −s + 1, . . . , s}, and the three leading-order terms of that of the self-energy operator Σσ(ε), pertaining to systems of spin-s fermions (s = a half-integer) in d-dimensional spatial space, interacting through an arbitrary two-body potential v(r − r ′ ). These contributions, which are expressed in terms at most of a three-body static ground-state correlation function, are amenable to accurate numerical calculation through employing correlated many-particle ground-state wavefunctions such as determined within, e.g., the quantum Monte Carlo framework. Such calculations will provide indisputably reliable information with regard to the spectral function of the single-particle excitations at high energies of correlated systems, as well as energy moments of this spectral function, and thus help to assess the reliability of theoretical approaches that are applied in studying such systems. We give especial attention to d = 3 and v ≡ vc, the long-range Coulomb potential, for which case we explicitly calculate the five leading-order terms of the regularized large-|ε| asymptotic series of Σσ(ε). Our considerations reveal some interesting aspects which are very specific to the behaviour of vc(r − r ′ ) both at small and large values of r − r ′ . In particular, we show that in these systems an inhomogeneity, even on the atomic scale, in the particle spin-polarization density gives rise to a pronounced effect, directly discernible in the inverse-photo-emission spectra; we show this effect to be absent in models with v bounded at origin and those in which v ≡ vc but Umklapp processes are neglected, unless the ground state possesses long-range magnetic order. Our analyses shed light on the importance of the non-local part of the self-energy operator and disclose that some of strictly non-local contributions to this, transform into local ones upon replacing v ≡ vc by vc, implying that a local approximation to Σσ(ε) that for v ≡ vc proves accurate, is necessarily less accurate for v ≡ vc. These findings establish a fundamental limitation of the so-called 'dynamical mean-field' approximation to Σσ(ε), which is strictly local, specifically in applications where v ≡ vc. We further explicitly establish some of the shortcomings of Σσ(ε) as calculated within the framework of the many-body perturbation theory. In this context we demonstrate the empirically well-known inadequacy of the dynamically-screened exchange self-energy operator in particular for describing the photo-emission and inverse photo-emission spectra of interacting systems at intermediate and large transfer energies and put forward a workable scheme that rids this self-energy of its fundamental defects. We present ample explicit analyses of our results in terms of uncorrelated many-body wavefunctions.

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Section: Sin(qr) (F34)mentioning

confidence: 89%

“…Whereas this is not the case according to the RPA for n(k) as calculated by Daniel and Vosko (1960), the n(k) due to Belyakov (1961) has the following form in the vicinity of k = k F (see text following Eq. (A70) in Appendix A)…”

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confidence: 93%

Dynamical correlation functions expressed in terms of many-particle ground-state wavefunction; the dynamical self-energy operator

Farid

2002

Philosophical Magazine B

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“…than v(E,,) is obtained for the homogeneous electron gas by noticing that the natural orbitals are in this case the plane wave states. Thus, the largest momentum that contributes to e,,, k,, is known from the momentum distribution, which has been obtained in the present approximation by Daniel and Vosko [33]. It is easily shown that in order to obtain E,, one only has to replace the integration limits in Eq.…”

Section: Resultsmentioning

confidence: 99%

A combined density functional and configuration interaction method

Savin

1988

Int. J. Quantum Chem.

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Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold u.The remaining part is obtained from a u-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.

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“…For this reason, we do not consider b|rpa = −0.170157 as being the converged value. (88); the results presented here correspond to nσ(k) ≡ n rpa σ (k) [95]. One observes that, although for sufficiently small rs, α − σ and α + σ approach towards the same value ασ, in contrast with the finding by Daniel and Vosko [95] this value is not equal to approximately 1.7, a value to which α − σ and α + σ are indeed relatively close for 10 −4< ∼ rs < ∼ 1.…”

Section: The Case Whenmentioning

confidence: 97%

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials inddimensions

Farid¹

2004

Philosophical Magazine

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We demonstrate that the skeleton of the Fermi surface Sf;σ pertaining to a uniform metallic ground state (corresponding to fermions with spin index σ) is determined by the Hartree-Fock contribution Σ hf σ (k) to the dynamic self-energy Σσ(k; ε). That is to say, in order for k ∈ Sf;σ, it is necessary (but for anisotropic ground states in general not sufficient) that the following equation be satisfied:where ε k stands for the underlying non-interacting energy dispersion and εf for the exact interacting Fermi energy. The Fermi surface Sf;σ consists of the set of k points which in addition to satisfying the above equation fulfilwhereThe set of k points which satisfy the first of the above two equations but fail to satisfy the second constitute the pseudogap region of the putative Fermi surface of the interacting system. We consider the behaviour of the ground-state momentum-distribution function nσ(k) for k in the vicinity of Sf;σ and show that, whereas for the uniform metallic ground states of the conventional single-band Hubbard Hamiltonian, described in terms of an on-site interaction, nσ(k − f;σ ) ≥ 1 2 and nσ(k + f;σ ) ≤ 1 2 (here k − f;σ and k + f;σ denote vectors infinitesimally close to Sf;σ, located respectively inside and outside the underlying Fermi sea), for interactions of non-zero range these inequalities can be violated (without thereby contravening the stability condition nσ(k − f;σ ) ≥ nσ(k + f;σ )). This aspect is borne out by the nσ(k) pertaining to the normal states of for instance liquid 3 He (corresponding to a range of applied pressure) as determined by means of quantum Monte Carlo calculations. We further demonstrate that for Fermi-liquid metallic states of fermions interacting through interaction potentials of non-zero range (e.g. the Coulomb potential), the zero-temperature limit of nσ(k) does not need to be equal to 1 2 for k ∈ Sf;σ; this in strict contrast with the uniform Fermi-liquid metallic states of the single-band Hubbard Hamiltonian (if such states at all exist). This aspect should be taken into account while analyzing the nσ(k) deduced from the angle-resolved photoemission data concerning real materials. We discuss, in the light of the findings of the present work, the growing experimental evidence with regard to the 'frustration' of the kinetic energy of the charge carriers in the normal states of the copper-oxide-based high-temperature superconducting compounds.

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Momentum Distribution of an Interacting Electron Gas

Cited by 193 publications

References 6 publications

Dynamical correlation functions expressed in terms of many-particle ground-state wavefunction; the dynamical self-energy operator

Dynamical correlation functions expressed in terms of many-particle ground-state wavefunction; the dynamical self-energy operator

A combined density functional and configuration interaction method

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials inddimensions

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