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

TL;DR

This paper presents an improved parametrization of the momentum distribution in the uniform electron gas, incorporating known limits and constraints, and discusses the cumulant expansion with exact limits.

Contribution

It introduces a new accurate parametrization of the momentum distribution n(k,r_s) that satisfies most known constraints and is valid for densities up to r_s ≈ 12.

Findings

The parametrization agrees with effective-potential calculations.

It is compatible with Quantum Monte Carlo data.

The paper derives exact limits for the cumulant expansion.

Abstract

The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k,r_s), with the momenta k measured in units of the Fermi wave number k_F and with the density parameter r_s, is constructed with the help of the convex Kulik function G(x). It is assumed that $n(0,r_s), n(1^\pm, r_s)$, the on-top pair density g(0,r_s) and the kinetic energy t(r_s) are known (respectively, from effective-potential calculations, 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,r_s), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculation of Takada and Yasuhara [1991 {\it Phys. Rev.} B {\bf 44} 7879], is compatible with Quantum Monte Carlo data, and is valid in the density range $r_s \lesssim 12$. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.