Tuning between collective dynamics and scrambling through initial-state symmetry alignment in long-range spin models

Abstract

Long-range interactions in many-body quantum systems give rise to a wide range of dynamical phenomena, from collective dynamics well described by integrable mean-field models with symmetric all-to-all couplings, to fast scrambling of quantum information from disordered long-range interactions. Here, we investigate scenarios in which both regimes emerge within a single deterministic, translation-invariant XY spin model with long-range couplings. We consider a sparse powers-of-two (PWR2) graph, where each spin interacts with a logarithmic number of neighbors, and a power-law-decaying model. By altering the initial state via local perturbations on a completely symmetric state, we show that the dynamics changes from collective to scrambling as witnessed by bipartite and multipartite entanglement measures. We characterize this collective-to-scrambling crossover using Lyapunov exponents in the semiclassical regime, and show that the spectral properties of the coupling graph adjacency matrix provide a very efficient tool to predict the onset of fast scrambling. Our results offer a unified framework for controlling the switch between collective and scrambling dynamics in a setup accessible in experiments with neutral atoms in cavities or in tweezer arrays.