A generalised Landau-Lifshitz equation for isotropic SU(3) magnet

TL;DR

This paper derives a generalized Landau-Lifshitz equation for isotropic SU(3) magnets, modeling large-scale fluctuations of magnetization and quadrupole moments using a quantum Hamiltonian and classical effective models on SU(3) coadjoint orbits.

Contribution

It introduces a novel generalized Landau-Lifshitz equation for SU(3) magnets based on a quantum Heisenberg model with biquadratic exchange, extending classical models.

Findings

Derived equations for large-scale fluctuations in SU(3) magnetic systems

Connected quantum Hamiltonian models to classical Hamiltonian systems on SU(3) orbits

Provided a framework for analyzing complex magnetic interactions

Abstract

In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the generalized Heisenberg Hamiltonian with biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of Lie group SU(3).