Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder

TL;DR

This paper introduces a classical SU(4) coherent state approach to approximate the dynamical spin structure factor of $S=1/2$ antiferromagnetic ladders, showing good agreement with quantum methods across various temperatures and couplings.

Contribution

The study develops a classical approximation method for quantum spin ladders using SU(4) coherent states, extending its validity across temperature ranges and coupling strengths.

Findings

Classical dynamics accurately reproduces quantum results at weak interdimer coupling.

High-temperature approximation remains valid even with strong interdimer coupling after rescaling.

Method shows promise for studying higher-dimensional weakly-coupled dimer systems.

Abstract

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.