  We consider quantum quenches in an integrable quantum chain with
tuneable-integrability-breaking interactions. In the case where these
interactions are weak, we demonstrate that at intermediate times after the
quench local observables relax to a prethermalized regime, which can be
described by a density matrix that can be viewed as a deformation of a
generalized Gibbs ensemble. We present explicit expressions for the
approximately conserved charges characterizing this ensemble. We do not find
evidence for a crossover from the prethermalized to a thermalized regime on the
time scales accessible to us. Increasing the integrability-breaking
interactions leads to a behaviour that is compatible with eventual
thermalization.
