Comparing Scattering Rates From Boltzmann And Dynamical Mean-Field Theory

We compute scattering rates for electrons in the two-dimensional Hubbard model for a one-orbital metal and Mott insulator and a two-orbital band insulator by means of dynamical mean-field theory (DMFT) and the Boltzmann scattering equation (BSE), which for the considered equilibrium scattering rates is equivalent to second order perturbation theory. As an intermediate method between both, we also consider the BSE without momentum conservation. In the weak interaction regime and for the band insulator, the last two agree to very good accuracy. The BSE with momentum conservation, on the other hand, shows slightly larger scattering rates, and a momentum differentiation of these on the Fermi surface. For the Mott insulator at strong interaction, the DMFT electron scattering rates are much larger and defy a BSE description. Noteworthy, the scattering rates for the band insulator are exceedingly small because-in contrast to the Mott insulator-impact ionization is not mediated by strong (density-density) Coulomb matrix elements.