Quasiconserved quantities in the perturbed spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> XXX model

We consider the isotropic spin-$1/2$ Heisenberg spin chain weakly perturbed by a local translationally- and $SU(2)$-invariant perturbation. Starting from integrals of motion unperturbed model, we modify them in order to obtain quasi-conserved (charges) for model. Such quantities are believed be responsible existence prethermalization phase at intermediate timescales. find that sufficiently perturbation indeed exist, construct an explicit form first few them.