  We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by
a local translationally- and SU(2)-invariant perturbation. Starting from the
local integrals of motion of the unperturbed model, we modify them in order to
obtain quasi-conserved integrals of motion (charges) for the perturbed model.
Such quasi-conserved quantities are believed to be responsible for the
existence of the prethermalization phase at intermediate timescales. We find
that for a sufficiently local perturbation only the first few integrals of
motion can be promoted to the quasi-conserved charges, whereas higher-order
integrals of motion do not survive.
