Low-energy peak in the one-particle spectral function of the electron gas at metallic densities

Based on a nonperturbative scheme to determine the self-energy Σ(k,iωₙ) with automatically satisfying the Ward identity and the total-momentum conservation law, a fully self-consistent calculation is done in the electron gas at various temperatures T to obtain G(k,iωₙ) the one-particle Green's function with fulfilling all known conservation laws, sum rules, and correct asymptotic behaviors; here, T is taken unprecedentedly low, namely, kBT/εF down to 10^-4 with εF the Fermi energy, and tiny mesh Δk as small as 10^-4kF is chosen near the Fermi surface in k space with kF the Fermi momentum. By analytically continuing G(k,iωₙ) to the retarded function GR(k,ω), we find a novel low-energy peak, in addition to the quasiparticle (QP) peak and one- and two-plasmon high-energy satellites, in the spectral function A(k,ω)[=-ImGR(k,ω)/π] for kBT10^-3εF in the simple-metal density region (2<rₛ<6 with rₛ the dimensionless density parameter). This new peak is attributed to the effect of excitonic attraction on Σ(k,iωₙ) arising from multiple excitations of tightly bound electron-hole pairs in the polarization function Π(q,iωq) for |q|≈2kF and |ωq|εF and thus it is dubbed ``excitron.'' Although this excitron peak height is only about a one-hundredth of that of QP, its excitation energy is about a half of that of QP for |k|≈kF, seemingly in contradiction to the Landau's hypothesis as to the one-to-one correspondence of low-energy excitations between a free Fermi gas and an interacting normal Fermi liquid. As for the QP properties, our results of both the effective mass m* and the renormalization factor z* are in good agreement with those provided by recent quantum Monte Carlo simulations and available experiments.