Classical spin dynamics based on SU($N$) coherent states

TL;DR

This paper develops a generalized classical spin dynamics framework based on SU(N) coherent states, improving the approximation of quantum spin system dynamics beyond traditional SU(2) models, especially for higher spin and complex interactions.

Contribution

It introduces a novel SU(N)-based classical dynamics approach that extends Landau-Lifshitz equations to better approximate quantum spin systems with larger local Hilbert spaces.

Findings

SU(N) coherent states improve quantum dynamics approximation

SU(3) dynamics better match exact results for S=1 models

Method applicable to complex multi-spin systems

Abstract

We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU($N$), where $N$ is the dimension of the local Hilbert space. This approach, that generalizes the well-known Landau-Lifshitz dynamics from SU(2) to SU($N$), provides a better approximation to the exact quantum dynamics for a large class of realistic spin Hamiltonians, including $S \geq 1$ systems with large single-ion anisotropy and weakly-coupled multi-spin units, such as dimers or trimers. We illustrate this idea by comparing the spin structure factors of a single-ion $S=1$ model that are obtained with the SU(2) and SU(3) classical spin dynamics against the exact solution.