Inelastic scattering and transient localization from coupling to two-level systems

We consider an electron interacting locally with two-level systems (TLSs) as an archetypal model for charge transport in the presence of inelastic scatterers. To assess the importance of quantum effects in the optical and dc conductivity we solve the model numerically using the finite temperature Lanczos method, and compare the results with both dynamical mean-field theory and the relaxation time approximation. In the slow fluctuation limit, the coupling to the TLSs causes transient localization of the carriers analogous to the one found in the electron-boson scattering problem, featuring enhanced resistivities and displaced Drude peaks. Fast inelastic scatterers suppress localization, restoring a more conventional regime where transport and optical properties are governed by independent scattering events.