Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
Maxime Dupont, Joel E. Moore
Abstract
The spin dynamics of strongly interacting one-dimensional quantum magnets at high-temperature displays an emergent coarse-grained hydrodynamic behavior, understood as the result of conserved quantities. Different kinds of emergent hydrodynamics can be characterized by the dynamical exponent $z$ governing the length-time scaling $x\ensuremath{\sim}{t}^{1/z}$. Relying on extensive numerical simulations, the authors extract the exponent $z$ for various microscopic quantum spin-$S$ models. They identify three universal regimes for the spin transport (superdiffusive with $z=3/2$, ballistic with $z=1$, and diffusive with $z=2$), which depend only on the isotropy and integrability of the system, but are independent of its microscopic details.