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,iw_n) 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,iw_n) 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, T/E_F down to 10⁻⁴ with E_F the Fermi energy, and tiny mesh as small as 10⁻⁴k_F is chosen near the Fermi surface in k space with k_F the Fermi momentum. By analytically continuing G(k,iw_n) to the retarded function G^R(k,w), 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,w)[= -Im G^R(k,w)/π] for T less than about 10⁻³E_F in the simple-metal density region (2<r_s<6 with r_s the dimensionless density parameter). This new peak is attributed to the effect of excitonic attraction on Σ(k,iw_n) arising from multiple excitations of tightly bound electron-hole pairs in the polarization function Π(q,iw_q) for |q| equal to about 2k_F and |w_q| << E_F 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| equal to about k_F, 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.