Far-from-equilibrium universality in two-dimensional Heisenberg antiferromagnets

We study the far-from-equilibrium dynamics of isolated two-dimensional Heisenberg antiferromagnets. We consider spin-spiral initial conditions which imprint a position-dependent staggered magnetization (or Neel order) in the two-dimensional lattice. Remarkably, we find a long-lived prethermal regime characterized by self-similar behavior of staggered magnetization fluctuations, although the system has no long-range order at finite energy and the staggered magnetization does not couple to conserved charges. By exploiting the separation of length scales introduced by the initial conditions, we derive an analytical model that allows us to compute the spatial-temporal scaling exponents and power-law distribution of the staggered magnetization fluctuations, and find excellent agreement with numerical simulations using phase-space methods. The scaling exponents are insensitive to details of the initial condition, in particular, no fine tuning of energy is required to trigger the self-similar scaling regime. Compared with recent results on far-from-equilibrium universality on the Heisenberg ferromagnet, we find quantitatively distinct spatial-temporal scaling exponents, therefore suggesting that the Heisenberg model can host different universal regimes depending on the initial conditions. Our predictions are relevant to ultracold-atom simulators of Heisenberg magnets and driven antiferromagnetic insulators.