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Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin

Yuefei Liu1,2,3, Olle Eriksson1,4, and Erik Sjöqvist1,*

  • *Contact author: erik.sjoqvist@physics.uu.se
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Phys. Rev. B 113, 134305 – Published 10 April, 2026

DOI: https://doi.org/10.1103/kf72-283n

Abstract

We examine the relation between the quantum Landau-Lifshitz equation (q-LL) [Wieser, Phys. Rev. Lett. 110, 147201 (2013)] and quantum Landau-Lifshitz-Gilbert equation (q-LLG) [Liu et al., Phys. Rev. Lett. 133, 266704 (2024)], two nonlinear purity preserving master equations that extend classical atomistic spin dynamics into the quantum regime. While the classical LL and LLG counterparts for any number of spins are known to be equivalent, i.e., give identical spin trajectories up to a rescaling of the time parameter, the quantum formulations are equivalent only in certain cases, such as for pure states or for arbitrary single spin-12 states. Here, we demonstrate that this equivalence breaks down even at the level of a single spin, provided s≥1. Focusing on a spin-1 particle in an anisotropic crystal field, we show that the q-LL and q-LLG equations generate inequivalent time evolution. We introduce temporal rescaling misfits that quantify the inequivalence of the two types of dynamics. Although our results highlight fundamental differences in dissipation mechanisms encoded in these equations, the resulting trajectories remain qualitatively similar for this system.

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Phys. Rev. B 113, 134305– Published 10 April, 2026
  • Received 3 December 2025
  • Accepted 24 March 2026
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