Classical and quantum spin dynamics of the honeycomb $\Gamma$ model

TL;DR

This paper compares classical and quantum spin dynamics in a frustrated honeycomb $b3$ model, revealing similarities in their dynamical structure factors and providing insights into the classical-quantum crossover in frustrated magnets.

Contribution

It introduces a combined analytical and numerical approach to compare classical and quantum spin dynamics in a frustrated system, highlighting the role of zero modes and precessional dynamics.

Findings

Low energy spectra are relaxational and constrained by zero modes.

Higher energy spectra exhibit precessional dynamics.

Quantum dynamical structure factors show features similar to classical predictions.

Abstract

Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a macroscopically-degenerate ground-state manifold, to the quantum spin liquid phase with fractionalized excitations. This is an important issue as we often encounter the demand for a sharp distinction between the classical and quantum spin liquid behaviors in real materials. Here we take the example of the classical spin liquid in a frustrated magnet with novel bond-dependent interactions to investigate the classical dynamics, and critically compare it with quantum dynamics in the same system. In particular, we focus on signatures in the dynamical spin structure factor. Combining Landau-Lifshitz dynamics simulations and the analytical Martin-Siggia-Rose (MSR) approach, we show that the low energy spectra are described by relaxational dynamics and highly constrained by the zero mode structure of the underlying degenerate classical manifold. Further, the higher energy spectra can be explained by precessional dynamics. Surprisingly, many of these features can also be seen in the dynamical structure factor in the quantum model studied by finite-temperature exact diagonalization. We discuss the implications of these results, and their connection to recent experiments on frustrated magnets with strong spin-orbit coupling.