Classical dynamics of the antiferromagnetic Heisenberg S=12 spin ladder

We employ a classical limit grounded in SU (4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the S=1/2 ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite-size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high-temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. Phys. Rev. B 109, 014427 (2024). We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly coupled dimers, situations that remain challenging for alternative numerical methods.