Oscillations Persist Exponentially Longer in Larger Complex Systems

Ángel L. Corps and colleagues at the Institute of Particle and Nuclear Physics investigate the emergence of time-translation symmetry breaking in a periodically driven Ising model with long-range interactions. Persistent period doubling arises from quantum many-body scars, a phenomenon where a small fraction of Floquet states exhibit non-thermal behaviour. The findings reveal how these scars, despite being a minority of states, can exponentially increase in number with system size and drive macroscopic, observable effects like period-doubling oscillations that persist for extended periods. The work offers insight into weak-ergodicity breaking and the complex dynamics of interacting quantum systems. Exponential growth of Floquet states unlocks strong time-crystal behaviour in the Ising model The number of time-translation symmetry breaking Floquet states now surpasses previous limits, growing exponentially in system size compared to earlier observations. Previous research into Floquet systems, those driven periodically in time, often encountered limitations in sustaining non-thermal behaviour. These limitations stemmed from the tendency of interacting quantum systems to thermalise, reaching equilibrium and losing any coherent, repeating patterns. Earlier observations of robust behaviour typically required the introduction of disorder, imperfections or randomness within the system, to suppress thermalisation and localize the quantum states. This localization prevented the system from averaging out the periodic drive, allowing for the emergence of time-crystal-like behaviour. However, the current study demonstrates a significant departure from this requirement. This exponential increase, crossing a threshold previously thought impossible without external disruption, enables persistent period-doubling oscillations, enduring for a time exponential in system size, a characteristic of Floquet time crystals. Floquet time crystals are a novel phase of matter exhibiting spontaneous time-translation symmetry breaking, meaning they exhibit periodic behaviour even in their ground state, driven by the external periodic force. The period doubling observed refers to the oscillation frequency being half that of the driving frequency, a common signature of symmetry breaking. The fact that this behaviour arises in a clean, precisely defined Ising model, without the need for disorder, is a crucial finding. The Ising model, a fundamental model in statistical mechanics, represents a system of interacting spins, each pointing either up or down, and serves as a simplified representation of magnetic materials. In this context, the ‘long-range interactions’ refer to the fact that spins can interact with each other across significant distances, unlike the nearest-neighbour interactions typically considered in simpler Ising models. The Ising model exhibits this behaviour under time-periodic kicking, revealing a link between the overlap of initial states and these special Floquet states. ‘Kicking’ refers to a specific type of periodic drive, involving short, strong pulses applied at regular intervals. The overlap between the initial state of the system and these Floquet states is a key indicator of how strongly the system is influenced by the symmetry-breaking states. These states organize into doublets displaying π-spectral pairing and long-range order, demonstrating a strong mechanism for sustained oscillations even within globally chaotic systems. The π-spectral pairing refers to the energy spectrum of the Floquet states, where pairs of states are separated by an energy gap of π (a fundamental constant in quantum mechanics), indicating a robust and stable configuration. An exponential increase in the number of Floquet states exhibiting time-translation symmetry breaking has been observed with system size, a sharp rise beyond previous limits. These previous limits required disorder to prevent thermalisation. This exponential growth enables persistent period-doubling oscillations, lasting a time exponential in system size, a hallmark of Floquet time crystals. These oscillations were observed for initial states containing both domain walls, boundaries between regions of differing magnetic alignment, and tilted spins, configurations where spins are not strictly aligned. Domain walls represent regions of instability within the magnetic material, while tilted spins introduce a degree of freedom that allows the system to respond more effectively to the periodic drive. Analysis revealed that these states organize into doublets displaying π-spectral pairing, indicated by a measurable spectral gap, and exhibit long-range order as evidenced by the eigenvalues of magnetization within each doublet. The eigenvalues of the magnetization, representing the strength and direction of the magnetic moment, provide a quantitative measure of the long-range order within the system, confirming that the spins are not randomly oriented but exhibit a coherent, collective behaviour. Sustained quantum oscillations emerge from order not disorder in magnetic systems Researchers at Berkeley and the Max Planck Institute of Quantum Optics are increasingly focused on harnessing non-equilibrium quantum phenomena for future technologies. The pursuit of stable, non-equilibrium states is crucial for developing novel quantum devices, such as quantum sensors and quantum memories. Traditionally, maintaining these states demanded introducing disorder into systems to prevent them from settling into predictable thermal states. This approach, while effective, often complicates the fabrication and control of quantum devices, as disorder can be difficult to engineer precisely and can introduce unwanted noise. A precisely defined Ising model, however, exhibited persistent oscillations, challenging the assumption that disorder is always necessary for such behaviour. Long-lasting, repeating patterns can emerge even without deliberately introducing randomness, potentially streamlining the design of future quantum technologies and broadening the scope of viable materials. This finding opens up new avenues for designing quantum systems that are inherently stable and robust, without relying on the artificial introduction of disorder. The observation of persistent period doubling in this periodically driven Ising model establishes a new route to stable, non-thermal behaviour, independent of disorder. The ability to achieve this behaviour in a clean system simplifies the design process and allows for greater control over the system’s properties. These repeating patterns link to specific Floquet states, the stable, repeating states a system settles into when regularly disturbed, that break time-translation symmetry, meaning their properties change over time. The Floquet states act as the ‘fingerprint’ of the time-crystal-like behaviour, encoding the information about the periodic drive and the system’s response. Crucially, the number of these symmetry-breaking states increases exponentially with system size, explaining the durability of the observed oscillations and exceeding previous expectations. This exponential scaling suggests that the time-crystal-like behaviour will become even more pronounced in larger systems, potentially leading to macroscopic quantum phenomena. The researchers observed persistent period doubling in a periodically driven Ising model, demonstrating stable oscillations without the need for deliberately introduced disorder. This is significant because maintaining stable, non-thermal states in quantum systems traditionally required disorder, which complicates device fabrication. The study reveals that these repeating patterns arise from specific Floquet states that break time-translation symmetry, and the number of these states grows exponentially with system size. This suggests the observed behaviour is robust and may become more pronounced in larger systems, offering a new pathway to designing stable quantum systems. 👉 More information🗞 Quantum many-body scars leading to time-translation symmetry breaking in kicked interacting spin models🧠 ArXiv: https://arxiv.org/abs/2604.20419 Tags: