Turbulent relaxation after a quench in the Heisenberg model

We predict the emergence of turbulent scaling in quench dynamics two-dimensional Heisenberg model for a wide range initial conditions and parameters. In isotropic model, we find that spin-spin correlation function exhibits universal consistent with energy cascade. When spin rotational symmetry is broken by an easy-plane exchange anisotropy, dual cascade emergent conserved charge associated to transverse magnetization fluctuations. The exponents are estimated analytically agree numerical simulations using phase space methods. also define (as energy, magnetization, number $S$) lead character cascade, insensitive microscopic details or conditions, suggests turbulence systems can be broadly realized cold atom solid-state experiments.