  We present a microscopic model for systems showing resistivity saturation. An
essentially exact quantum Monte-Carlo calculation demonstrates that the model
describes saturation. We give a simple explanation for saturation, using charge
conservation and considering the limit where thermally excited phonons have
destroyed the periodicity. Crucial model features are phonons coupling to the
hopping matrix elements and a unit cell with several atoms. We demonstrate the
difference to a model of alkali-doped C60 with coupling to the level positions,
for which there is no saturation.
