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

Quasi-conserved quantities in the perturbed XXX spin chain