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Quasi-conserved charges in the perturbed spin-1/2 XXX model

We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationallyand 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 the quasi-conserved quantities indeed exist, and we construct an explicit form for the first few of them.