Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

We address the nature of spin dynamics in various integrable and\nnon-integrable, isotropic and anisotropic quantum spin-$S$ chains, beyond the\nparadigmatic $S=1/2$ Heisenberg model. In particular, we investigate the\nalgebraic long-time decay $\\propto t^{-1/z}$ of the spin-spin correlation\nfunction at infinite temperature, using state-of-the-art simulations based on\ntensor network methods. We identify three universal regimes for the spin\ntransport, independent of the exact microscopic model: (i) superdiffusive with\n$z=3/2$, as in the Kardar-Parisi-Zhang universality class, when the model is\nintegrable with extra symmetries such as spin isotropy that drive the Drude\nweight to zero, (ii) ballistic with $z=1$ when the model is integrable with a\nfinite Drude weight, and (iii) diffusive with $z=2$ with easy-axis anisotropy\nor without integrability, at variance with previous observations.\n