Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

Abstract

The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k, rs), with the momenta k measured in units of the Fermi wave number kF and with the density parameter rs, is constructed with the help of the convex Kulik function G(x). It is assumed that n(0, rs), n(1 ± , rs), the on-top pair density g(0, rs) and the kinetic energy t(rs) are known (respectively, from accurate calculations for rs = 1, ..., 5, from the solution of the Overhauser model, and from Quantum Monte Carlo calculations via the virial theorem). Information from the high-and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k, rs), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculations of Takada and Yasuhara [Phys. Rev. B 44, 7879 (1991)], is compatible with Quantum Monte Carlo data, and is valid in the density range rs 12. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.

Performance of one-body reduced density-matrix functionals for the homogeneous electron gas

“…This behavior is in complete analogy to the case of finite systems for the Müller functional. Unfortunately, it is in conflict with the fact that the exact momentum distribution 29,30 is a monotonically decreasing function of k and is strictly smaller than 1, i.e., there are no pinned states. Additionally, the exact momentum distribution is concave for k Ͻ k F , it shows a discontinuity at k F , and for k Ͼ k F , it goes to zero asymptotically.…”

“…Both the size and the dependence on r s are in complete disagreement with the exact theory, where ⌬n is substantially bigger and decreases with r s , as one can see from the two fits to the diffusion Monte Carlo ͑DMC͒ data. 29,30 We now turn to the question of state pinning. As we see in Fig.…”

Emergence of an excitonic collective mode in the dilute electron gas

“…(54) and (55) and compared with G RA n (q, iω), the parametrized form for G n (q, iω) due to RA, to find that G RA n (q, iω) is in fact very reliable; in particular, no appreciable difference can be seen for the quantities given by integrals over q and ω, such as ε c (r s ) obtained through the adiabatic connection formula, Eq. (27) in Ref. 29, in which we have calculated with use of either G s (q, iω) + G RA n (q, iω) or…”

“…Confronted with this difficulty, we will take the following strategy; firstly, we reconsider the parametrization scheme for determining n(p) due to Gori-Giorgi and Ziesche (GZ), 27 who interpolate the accurate data for n(p) in the effective potential expansion (EPX) method 9 for 1 ≤ r s ≤ 5 with that in the Wigner-crystal limit (r s ≫ 10), together with the two sum rules, one for the total number and the other for the total kinetic energy, 9 expressed as…”

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

“…1). We have also determinedμ c;σ by employing a very recent parametrized expression for n σ (k), asserted by Gori-Giori and Ziesche [100] to be valid in the range r s < ∼ 12, and observed no resemblance whatever between thisμ c;σ and the aforementioned quantum-Monte-Carlobasedμ c;σ over the entire range r s < ∼ 12 (see caption of Fig. 2).…”