Nonlinear quantum multi-spin dynamics without entanglement

Abstract

We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin $s$, based on a variational product-state \textit{ansatz} that includes both pure and mixed local states. By construction, intersite entanglement -- expected to remain negligible even on very short time scales in many real materials -- is excluded, while local quantum effects are retained through the nonclassical structure of $s\ge 1$ density operators. Nonlinear dynamics arise from both the mean-field interdependence of the local states and the state-dependent dissipative terms. The framework recovers classical spin dynamics for $s=\frac{1}{2}$ while allowing genuinely quantum local dynamics for higher spins. It clarifies the variational and geometric origin of the inequivalence between quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics, provides a criterion for their equivalence under a common time rescaling, establishes connections with the classical theory through two qualitatively distinct limits ($s\to \infty$ and a large number of quantum spins $N$), and allows realistic $\mathcal{O}(N)$ simulations of quantum spin dynamics in materials.