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≥ 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=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→∞ and a large number of quantum spins N), and allows realistic 𝒪(N) simulations of quantum spin dynamics in materials.
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BibTeX
@misc{miranda2026nonlinear,
title = {{Nonlinear quantum multi-spin dynamics without entanglement}},
author = {Ivan P. Miranda and Erik Sjöqvist},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05521},
eprint = {2610.05521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05521},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonlinear quantum multi-spin dynamics without entanglement
AU - Ivan P. Miranda
AU - Erik Sjöqvist
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.05521
UR - https://arxiv.org/abs/2610.05521
AB - 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≥ 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=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→∞ and a large number of quantum spins N), and allows realistic 𝒪(N) simulations of quantum spin dynamics in materials.
ER -