Spin diffusion probe of magnetization frustration

We develop a diffusive framework to describe finite-temperature dynamics in $J_1$-$J_2$ Heisenberg model, and propose that spin diffusion constant can serve as a probe of the frustration. Using a SLN approach, we derive an analytic form of the dynamical correlation function that depends solely on the spin diffusion constant $\gamma$. Comparison with large-scale spin-dynamics simulations on the order of $10^4$ spins demonstrates excellent agreement across all timescales and momentum scales. The phase diagram of $\gamma$ is further consistent with that obtained from the spin correlation length, indicating that our model captures the full finite-temperature behavior. To test its universality, we compute the spin conductivity $\sigma_s$ and susceptibility $\chi$ via the Kubo formula and find that $\sigma_s/\chi$ coincides with $\gamma$, even without assuming diffusive transport. These results establish the spin diffusion constant as a quantitative measure of frustration in magnetic systems.