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arXiv:2610.28462

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

Sridevi Kuriyattil, Johannes Kombe, Andrew J. Daley, Pablo M. Poggi

quant-phSubmitted Oct 20, 2026• Announced Oct 21, 2026• 0 citations
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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.

Comments
20 pages, 11 figures in the main text, and 6 figures in the appendices

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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.
In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size.This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes.In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity.In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior.We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space.This mapping predicts mean-field critical exponents ν = -1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics.In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.
We investigate the integrability-to-chaos transition and information scrambling in Ising spin networks via a graph-theoretic formulation. Modeling spins as vertices and interactions as edges encoded by adjacency matrices across path, Erdos-Renyi, and Watts-Strogatz topologies, we demonstrate that long-range couplings and heterogeneous degree distributions markedly accelerate quantum information propagation. The Hamiltonian comprises local and normalized non-local interactions; tuning the non-local coupling and field heterogeneity drives integrability breaking. To quantify scrambling, we employ bipartite mutual and tripartite information. Increasing non-local interactions drives tripartite information to large negative values, signaling deep information scrambling. The squared commutators constructed from out-of-time-order correlators (OTOCs) exhibit early-time exponential growth; equivalently, the OTOC four-point functions themselves decay exponentially, yielding quantum Lyapunov exponents that scale systematically with parameters governing the chaotic regime. Complementing this, Krylov complexity reveals rapid operator growth in the chaotic phase, synchronizing with OTOC and mutual information dynamics. Spectrally, the transition manifests as a shift from Poissonian to Wigner-Dyson level spacing statistics. The spectral form factor (SFF) exhibits the characteristic slope-dip-ramp-plateau structure, enabling the extraction of Thouless and Heisenberg times. Crucially, a reduced Thouless time strongly correlates with accelerated information and operator scrambling. Ultimately, this work establishes a unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics, offering insights into thermalization and non-equilibrium dynamics in quantum many-body systems.
Entanglement is a defining feature of many-body quantum systems and is an essential requirement for quantum computing. It is therefore useful to study physical processes which generate entanglement within a large system, as they maybe replicated for applications involving the said requirements in quantum information processing. A possible avenue to maximize entanglement generation is to rely on the phenomena of information scrambling, i.e. transport of initially localized information throughout the system. Here the rationale is that the spread of information carries with it an inherent capacity of entanglement generation. Scrambling greatly depends upon the dynamical nature of the system Hamiltonian, and the interplay between entanglement generation and information scrambling maybe investigated taking a chain of interacting spins on a one dimensional lattice. This system is analogous to an array of qubits and this relative simplicity implies that the resulting unitary dynamics can be efficiently simulated using present-day cloud based NISQ devices. In our present work, we consider such a spin model which is made up of nearest and next nearest neighbor XXZ Model, along with an introduced coupling term λ. This coupling term serves as a tuning parameter which modifies the dynamical nature of the system from the integrable to the quantum chaotic regime. In order to quantify the entanglement generated within the system we use the more general multipartite metric which computes the average entanglement across all system bipartitions to obtain a global picture of the entanglement structure within the entire system. Further to make our study initial state independent, we consider an ensemble of random initial states and evaluate the multipartite entanglement generated for each of these states under time evolution. We find clear differences in the entanglement measures as the system undergoes through different regimes. We also analyze the fluctuations present within our entanglement metric and find a distinct pattern as we head from the integrable to the chaotic regime.
We study the competing effects of collective generalized measurements and interaction-induced scrambling in the dynamics of an ensemble of spin-1/2 particles at the level of quantum trajectories. This setup can be considered as analogous to the one leading to measurement-induced transitions in quantum circuits. We show that the interplay between collective unitary dynamics and measurements leads to three regimes of the average Quantum Fisher Information (QFI), which is a witness of multipartite entanglement, as a function of the monitoring strength. While both weak and strong measurements lead to extensive QFI density (i.e., individual quantum trajectories yield states displaying Heisenberg scaling), an intermediate regime of classical-like states emerges for all system sizes where the measurement effectively competes with the scrambling dynamics and precludes the development of quantum correlations, leading to sub-Heisenberg-limited states. We characterize these regimes and the crossovers between them using numerical and analytical tools, and discuss the connections between our findings, entanglement phases in monitored many-body systems, and the quantum-to-classical transition.
We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.
Motivated by recent experimental realizations of programmable spin models with long-range interactions, we investigate the non-equilibrium dynamics of the Power-of-Two (PWR2) model. This model consists of sparse long-range couplings between spin-1/21/21/2 objects separated by d=2nd = 2^nd=2n. In the absence of disorder, the system exhibits rapid scrambling and fast thermalization. We explore the impact of disorder in this system by analyzing the time evolution of the survival probability, half-chain entanglement entropy, and out-of-time-ordered correlators (OTOCs). We find that sufficiently strong disorder suppresses information spreading and induces localization. Remarkably, in the strong-disorder regime, the OTOCs display a non-monotonic spatial profile arising from the intrinsic nonlocality of the interactions, signaling qualitatively distinct scrambling dynamics compared to conventional long-range interacting systems. To characterize the localization transition, we extract the critical disorder strength hch_chc​ from the spectral statistics and the eigenstate entanglement. We observe that hch_chc​ increases with system size. Furthermore, at a fixed disorder strength, the eigenstate-averaged entanglement entropy increases with system size, while the inverse participation ratio decreases, indicating enhanced delocalization at larger sizes. These results collectively suggest that the PWR2 model remains ergodic in the thermodynamic limit for any finite disorder strength.