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

Abstract

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^{-4}k_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^{-3}E_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.

26 pages, 22 figures with 23 figure files in eps

References in corpus (25)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Angle-resolved photoemission spectroscopy
• Electronic Density Response of Warm Dense Matter
• Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas
• Emergence of an excitonic collective mode in the dilute electron gas
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Quantum critical metals in $4-\epsilon$ dimensions
• Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter
• The electron lifetime in Luttinger liquids
• Constraint-based Wavevector- and Frequency-dependent Exchange-Correlation Kernel of the Uniform Electron Gas
• Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
• Prediction of a roton-type feature in warm dense hydrogen
• Vertex corrections for positive-definite spectral functions of simple metals
• The GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas
• Analysis of dynamical effects in the uniform electron liquids with the self-consistent method of moments complemented by the Shannon information entropy and the path-integral Monte-Carlo simulations
• Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo
• First-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium at all densities
• Realizing infrared power-law liquids in the cuprates from unparticle interactions
• Superconductivity in the Uniform Electron Gas: Irrelevance of Kohn-Luttinger Mechanism
• Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function
• Lifetime of quasi-particles in the nearly-free electron metal Sodium
• Observation of non-Fermi liquid physics in a quantum critical metal via quantum loop topography
• QMC-consistent static spin and density local field factors for the uniform electron gas