Universal prethermal dynamics and self-similar relaxation in the two-dimensional Heisenberg model

We characterize the universal far-from-equilibrium dynamics of the isolated two-dimensional quantum Heisenberg model. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states as well as values of magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in non-equilibrium $O(n)$ field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes which remain gapless at long times and which are protected by the global SU(2) symmetry. Our predictions, which suggest a new non-equilibrium universality class, are readily testable in ultra-cold atoms simulators of Heisenberg magnets.