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We show that Quantum-Monte-Carlo calculations of the dynamic structure factorof the isotropic spin-1/2 antiferromagnetic chain at intermediate temperaturescorroborate a picture of diffusive spin dynamics at finite frequencies in thelow-energy long wave-length limit and are in good agreement with recentpredictions for this by J. Sirker, R. G. Pereira, and I. Affleck[arXiv:0906.1978v1].

Hydrodynamic Limit for the Spin Dynamics of the Heisenberg Chain