Fate of diffusion under integrability breaking of classical integrable magnets

Abstract

Diffusive transport is a ubiquitous phenomenon, yet the microscopic origin of diffusion in interacting physical systems remains a challenging question, irrespective of whether quantum effects are dominant or not. In this work, we study infinite temperature spin diffusion in a classical integrable, space-time discrete version of anisotropic Landau-Lifshitz magnet in the easy-axis regime, subjected to integrability-breaking perturbations. Our numerical results based on large-scale simulations reveal i) a sharp change in the spin diffusion constant as a function of perturbation strength in the thermodynamic limit and ii) a crossover from non-Gaussian to Gaussian statistics of magnetization transfer reflected in higher order cumulants under integrability breaking. Both our observations hint to the presence of non-trivial diffusion mechanism inherent to integrable systems.

Figures (7)

• Figure 1: Time-dependent diffusion constant $D_L(t)$ versus $t$ in model $A$ for different system size $L$ for (a) $\epsilon = 0$ and (b) $\epsilon = 0.005$
• Figure 2: $D_L(t)$ versus $\epsilon^2 t$ for different $\epsilon$ in (a) model $A$ and (b) model $B$. System size $L = 2^{17}$; $\epsilon \in [0, 0.02]$ in (a) and $\epsilon \in [0, 0.04]$ in (b), with color ranging from yellow to blue as $\epsilon$ increases.
• Figure 3: $D(t=L/2)$ versus $\sqrt{L} \epsilon$ for different $L$ in (a) model $A$ and (b) model $B$.
• Figure 4: Rescaled cumulants of the cumulative current, $\kappa_n(t)$, for different values of $\epsilon$ in model A for system size $L=2^{20}$.
• Figure 5: Time-dependent diffusion constant $D_L(t)$ versus $t$ in model $B$ for different system size $L$ for (a) $\epsilon = 0$ and (b) $\epsilon = 0.01$.