  The electron dynamics in metals are usually well described by the
semiclassical approximation for long-lived quasiparticles. However, in some
metals, the scattering rate of the electrons at elevated temperatures becomes
comparable to the Fermi energy; then, this approximation breaks down, and the
full quantum-mechanical nature of the electrons must be considered. In this
work, we study a solvable, large-$N$ electron-phonon model, which at high
temperatures enters the non-quasiparticle regime. In this regime, the model
exhibits "resistivity saturation" to a temperature-independent value of the
order of the quantum of resistivity - the first analytically tractable model to
do so. The saturation is not due to a fundamental limit on the electron
lifetime, but rather to the appearance of a second conductivity channel. This
is suggestive of the phenomenological "parallel resistor formula", known to
describe the resistivity of a variety of saturating metals.
