Temperature dependence of the quasiparticle weight in metals with local self-energy

Recently it was demonstrated that the temperature dependence of the quasiparticle weight $Z$ in metals with local self-energy is experimentally measurable [A. Hunter et al., Phys. Rev. Lett. 131, 236502 (2023)]. Motivated by this finding, we study the quasiparticle properties of metals with phenomenological electron-electron interaction described by the Eliashberg function ${\ensuremath{\alpha}}^{2}F(y)$ scaling as ${y}^{\ensuremath{\beta}}$ in the limit of low energies $y$. We show that the temperature dependence of $Z$ is nonuniversal and strongly depends, inter alia, on the value of the exponent $\ensuremath{\beta}$. The validity of the recently introduced ``power-law liquid ansatz'' for the frequency and temperature dependence of the quasiparticle lifetime is studied within the same model as well.