Quantum fluctuations and chaos in fully connected spin models
Abstract Overview
This paper studies beyond-mean-field dynamics in a fully connected SU(3) spin-exchange model, with emphasis on how quantum fluctuations modify chaotic macroscopic behavior. Using the two-particle irreducible (2PI) effective action formalism and a 1/L expansion, the authors derive self-consistent equations of motion for two-point functions that include interaction-generated higher-order correlations through memory terms. They compare this approach with mean-field theory and a second-order cumulant expansion, and use trajectory divergence of collective spin observables to map a dynamical phase diagram. The analysis shows that fluctuations can suppress or soften chaos, especially at small system size or strong interaction, and that low-order cumulant truncation misses important correlation feedback in these regimes.
Novelty
The distinctive contribution is the application of a next-to-leading-order 2PI 1/L expansion to a fully connected SU(3) spin model to study chaos beyond mean field in a self-consistent way. The work specifically highlights fluctuation-induced regularization of chaotic macroscopic dynamics and contrasts it with the limitations of fixed-order cumulant closures.
Results
The authors identify a dynamical phase structure with regular regions near integrable limits, a regime where the second-order cumulant expansion predicts chaos but the NLO 2PI treatment regularizes it, and a regime where chaos persists but with a reduced Lyapunov growth rate. They also show that the NLO 2PI approach departs from mean-field behavior earlier for smaller systems and captures relaxation of bosonic level populations in a case where the second-order cumulant expansion instead produces persistent oscillations.
Key Points
- A self-consistent 2PI framework is derived for the fully connected SU(3) model, with memory terms that encode the feedback of higher-order correlations on two-point dynamics.
- Quantum fluctuations controlled by interaction strength and system size can regularize or soften chaotic macroscopic trajectories, reshaping the dynamical phase diagram relative to mean-field expectations.
- Compared with the second-order cumulant expansion, the NLO 2PI method better captures strong-fluctuation behavior, including earlier deviation from mean field and relaxation of level populations.