Resistivity saturation in a tractable model

We present a tractable large N electron phonon model that displays resistivity saturation At low temperatures the resistivity obeys the semiclassical linear in temperature law that breaks down at the Mott Ioffe Regel limit where the scattering rate is comparable to the Fermi energy At higher temperatures the resistivity saturates to a value independent of the electron phonon coupling strength Our model exhibits a natural emergence of two qualitatively different conductivity channels reminiscent of the phenomenological parallel resistor formula We also present numerical results showing that these results extend to finite values of N Werman and Berg PRB 93 075109