Anomalous Lifetime of Quasiparticles in Fermi Liquids as a Precursor of the Density-Wave Instability

We analytically study the inelastic lifetime of quasiparticles due to particle-particle interactions in a three-dimensional Fermi liquid approaching a density-wave instability. Using the G₀W approximation, we find that the softening of the dielectric function significantly enhances the quasiparticle decay rate near the instability. While the zero-temperature quasiparticle lifetime at the Fermi surface generally follows a |εₖ-εF|-α divergence with α=2, we observe α=0.5 at the instability point and α=1 within the density-wave phase. Moreover, we demonstrate that the renormalization constant Z is substantially suppressed as the instability is approached, enhancing the effective mass. We extend our analysis to ultra-cold Rydberg-dressed Fermi liquids, where the soft-core interactions promote density-wave instability, and find that our numerical G₀W results are in excellent agreement with our analytic predictions for quasiparticle lifetime, renormalization constant, and effective mass.