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

TL;DR

This paper analytically investigates how quasiparticle lifetimes in a three-dimensional Fermi liquid are affected near a density-wave instability, revealing anomalous decay rates and mass enhancements that could be observed in ultra-cold Rydberg-dressed Fermi gases.

Contribution

The study provides the first analytical and numerical analysis of quasiparticle lifetime divergence and effective mass enhancement near a density-wave instability in Fermi liquids.

Findings

Quasiparticle lifetime diverges with an exponent of 0.5 at the instability.

Renormalization constant Z is suppressed near the instability.

Results agree well with numerical G0W calculations for Rydberg-dressed Fermi liquids.

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 $|\varepsilon_k-\varepsilon_{\rm F}|^{-\alpha}$ 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.