Anomalous Lifetime of Quasiparticles in Fermi Liquids

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 $G_0W$ 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 as $|\epsilon_k-\epsilon_F|^{-\alpha}$ divergence with $\alpha = 2$, we observe $\\alpha= 1/2$ at the instability

point and $\alpha= 1$ 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 $G_0W$ results are in excellent agreement

with our analytic predictions for quasiparticle lifetime, renormalization constant, and effective

mass.