Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

The stranglehold of low temperatures on fascinating quantum phenomena in\none-dimensional quantum magnets has been challenged recently by the discovery\nof anomalous spin transport at high temperatures. Whereas both regimes have\nbeen investigated separately, no study has attempted to reconcile them. For\ninstance, the paradigmatic quantum Heisenberg spin-$1/2$ chain falls at low\ntemperature within the Tomonaga-Luttinger liquid framework, while its\nhigh-temperature dynamics is superdiffusive and relates to the\nKardar-Parisi-Zhang universality class in $1+1$ dimensions. This Letter aims at\nreconciling the two regimes. Building on large-scale matrix product state\nsimulations, we find that they are connected by a temperature-dependent\nspatiotemporal crossover. As the temperature $T$ is reduced, we show that the\nonset of superdiffusion takes place at longer length and timescales $\\propto\n1/T$. This prediction has direct consequences for experiments including nuclear\nmagnetic resonance: it is consistent with earlier measurements on the nearly\nideal Heisenberg $S=1/2$ chain compound Sr$_2$CuO$_3$, yet calls for new and\ndedicated experiments.\n