Turbulent relaxation after a quench in the Heisenberg model

Abstract

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

6+2 pages, 3+2 figures

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Cited by in corpus (6)

• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Far-from-equilibrium universality in the two-dimensional Heisenberg model
• Non-equilibrium Bose-Einstein Condensation
• Transverse instability and universal decay of spin spiral order in the Heisenberg model
• Far-from-equilibrium universality in two-dimensional Heisenberg antiferromagnets
• A Simple XY Model for Cascade Transfer