Apparent Planckian scattering from local polaron formation

We propose a simple mechanism for apparent Planckian scattering based on local polaron formation, in which $\Gamma_\text{tr} = \Gamma_0 + \alpha k_BT / \hbar$ with $\alpha \sim O(1)$ emerges from quasielastic scattering without fine tuning. We provide evidence for our proposal in Monte Carlo simulations of the Holstein model with disordered electron-phonon coupling in the adiabatic limit. Our mechanism generates a finite interval of couplings in which the slope $\alpha$ is approximately constant, coinciding with the onset of local polaron formation. In this regime, Matthiessen's rule is dramatically violated (or obeyed, depending on one's point of view) in that changes to the couplings, which in perturbation theory would alter the slope $\alpha$, instead change the intercept $\Gamma_0$. We conjecture that a version of our mechanism applies to any system with a dominant disordered interaction that can drive polaron formation. This potentially includes regimes of the recently introduced disordered-Yukawa-coupling strange metal models where polaron formation is not suppressed.