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

Abstract

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${}_0$W 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 $|{\epsilon }_k-{\epsilon }_{\mathrm{F}}{|}^{-\alpha }$ divergence with $\alpha =2$, we observe $\alpha =0.5$ 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${}_0$W results are in excellent agreement with our analytic predictions for quasiparticle lifetime, renormalization constant, and effective mass.

5.5 pages, 4 figures (Supplemental: 3.5 pages, 1 figure); Submitted