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arXiv:2607.12355

From stable periodic orbits to many-body chaos: doubly tunable prethermalization via engineering of an emergent band structure

Jianan Wang, Yang Hou, Andrea Pizzi, Johannes Knolle, Roderich Moessner, Hongzheng Zhao

cond-mat.stat-mechcond-mat.quant-gasquant-phSubmitted Jul 14, 2026• Announced Jul 15, 2026• 0 citations
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Abstract

We uncover a family of many-body periodic orbits in a periodically driven (Floquet) spin system away from the high-frequency limit. While linear stability analysis predicts that perturbed many-body trajectories remain close to stable periodic orbits, thermodynamic principles dictate that Floquet heating will ultimately set in. Our work aims to resolve the tension between these two expectations. In particular, we show that perturbations away from the stable periodic orbits feature a description akin to a quasiparticle band structure. A long-lived prethermal regime appears when modes around the gapless point are slowly populated. The dispersion determines the prethermal lifetime, and we show how band engineering leads to a "doubly tunable" parametric dependence of the prethermal lifetime $R^{-W}$, with $R$ the width in momentum space of the quasiparticle distribution and $W$ the exponent of the dispersion around the gapless point. Our results not only establish a powerful route toward stabilizing non-equilibrium phases of matter in driven many-body systems but also establish a conceptual bridge between periodic orbits in 'low-dimensional' nonlinear systems and many-body chaos.

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We uncover a family of many-body periodic orbits in a periodically driven (Floquet) spin system away from the high-frequency limit. While linear stability analysis predicts that perturbed many-body trajectories remain close to stable periodic orbits, thermodynamic principles dictate that Floquet heating will ultimately set in. Our work aims to resolve the tension between these two expectations. In particular, we show that perturbations away from the stable periodic orbits feature a description akin to a quasiparticle band structure. A long-lived prethermal regime appears when modes around the gapless point are slowly populated. The dispersion determines the prethermal lifetime, and we show how band engineering leads to a "doubly tunable" parametric dependence of the prethermal lifetime R−WR^{-W}R−W, with RRR the width in momentum space of the quasiparticle distribution and WWW the exponent of the dispersion around the gapless point. Our results not only establish a powerful route toward stabilizing non-equilibrium phases of matter in driven many-body systems but also establish a conceptual bridge between periodic orbits in 'low-dimensional' nonlinear systems and many-body chaos.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability with respect to random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are nonuniversal: we observe Fermi's golden rule scaling, power-law scaling inconsistent with the golden rule, and non-power-law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase the temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
Non-equilibrium dynamics of strongly and rapidly driven quantum many-body systems is poorly understood beyond periodic driving, where heating is exponentially slow in the drive frequency (Floquet Prethermalization). In contrast, non-periodic drives were found to exhibit widely different heating scalings with no unifying principle. This work identifies a resonance-suppression principle governing slow heating up to a prethermal lifetime τ∗τ_*τ∗​: When the drive's spectral arithmetic structure restricts multiphoton resonances, τ∗τ_*τ∗​ is controlled by low-frequency spectral suppression. The principle distinguishes (i) Single-photon suppression, quantified by a low-frequency suppression law f(Ω)f(Ω)f(Ω) for the drive's Fourier Transform weight near Ω=0Ω=0Ω=0, from (ii) Multi-photon suppression, where nested commutators remain controlled if exceptional arithmetic structure satisfies a subadditive property. Remarkably, if multi-photon suppression holds, τ∗τ_*τ∗​ scaling with drive speed λλλ is governed by f(Ω)f(Ω)f(Ω). This law of τ∗τ_*τ∗​ is found through a small-divisor mechanism in this work's iterative rotating frame scheme. Multi-photon suppression breakdown separates λλλ-scaling of τ∗τ_*τ∗​ in linear response and non-perturbative theory, shown by a case study of Quasi-Floquet driving. The principle is applied to (i) Resolve inconsistencies in literature on non-periodic driving, and (ii) Provide design principles for engineering prethermal phases of matter in programmable quantum simulators, exemplified by new non-periodic `Factorial' drives with tunable τ∗τ_*τ∗​.
We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet's theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.
Periodically driven (Floquet) systems are said to prethermalize when their energy absorption is very slow for a long time. This effect was first discovered in quantum spin models, where the heating rate is exponentially small in the ratio between the driving frequency and the spin bandwidth. Recently, it was shown that prethermalization occurs also in classical systems with an infinite bandwidth. Here, we address the open question of which small parameter controls the lifetime of the prethermal state in these systems. We show that the lifetime is controlled by the temperature of the prethermal state, which is quasiconserved when the heating is slow. We substantiate this finding in systems of periodically driven coupled rotors, by studying the dependence of the prethermal lifetime on both the initial conditions and the connectivity. This result allows us to develop a simple analytical model that describes the crossover from prethermalization to chaos in many-body classical systems.
We study the regimes of heating in the periodically driven O(N)-model, which is a well established model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green's function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the system ceases to absorb, and at parametrically late times a thermalizing regime. Our simulations suggest that in the thermalizing regime the absorbed energy grows algebraically in time with an exponent that approaches the universal value of 1/2, and is thus significantly slower than linear Joule heating. Our results demonstrate the parametric stability of prethermal states in a many-body system driven at frequencies that are comparable to its microscopic scales. This paves the way for realizing exotic quantum phases, such as time crystals or interacting topological phases, in the prethermal regime of interacting Floquet systems.