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Fundamental conservation laws predict ballistic, i.e., dissipationlesstransport behaviour in one-dimensional quantum magnets. Experimental evidence,however, for such anomalous transport has been lacking ever since. Here weprovide experimental evidence for ballistic heat transport in a S=1/2Heisenberg chain. In particular, we investigate high purity samples of thechain cuprate SrCuO2 and observe a huge magnetic heat conductivity$\kappa_{mag}$. An extremely large spinon mean free path of more than amicrometer demonstrates that $\kappa_{mag}$ is only limited by extrinsicscattering processes which is a clear signature of ballistic transport in theunderlying spin model.

Ballistic heat transport of quantum spin excitations as seen in SrCuO2