The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, nonintegrable systems typically thermalize to an effectively infinite-temperature state, losing all memory of their initial states. However, in the presence of a large time-periodic Floquet drive, there exist special points in phase space where the strongly interacting system develops approximate emergent conservation laws. Here, we present results for an exactly solvable model of two coupled chaotic quantum dots with multiple orbitals interacting via random two- and four-fermion interactions in the presence of a Floquet drive. We analyze the phenomenology of dynamically generated freezing using a combination of exact diagonalization and field-theoretic analysis in the limit of a large number of electronic orbitals. The model displays universal freezing behavior irrespective of whether the theory is averaged over the disorder configurations or not. We present explicit computations for the growth of many-body chaos and entanglement entropy, which demonstrates the long-lived coherence associated with the interacting degrees of freedom even at late times at the dynamically frozen points. We also compute the slow timescale that controls relaxation away from exact freezing in a high-frequency expansion.
The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, nonintegrable systems typically thermalize to an effectively infinite-temperature state, losing all memory of their initial states. However, in the presence of a large time-periodic Floquet drive, there exist special points in phase space where the strongly interacting system develops approximate emergent conservation laws. Here, we present results for an exactly solvable model of two coupled chaotic quantum dots with multiple orbitals interacting via random two- and four-fermion interactions in the presence of a Floquet drive. We analyze the phenomenology of dynamically generated freezing using a combination of exact diagonalization and field-theoretic analysis in the limit of a large number of electronic orbitals. The model displays universal freezing behavior irrespective of whether the theory is averaged over the disorder configurations or not. We present explicit computations for the growth of many-body chaos and entanglement entropy, which demonstrates the long-lived coherence associated with the interacting degrees of freedom even at late times at the dynamically frozen points. We also compute the slow timescale that controls relaxation away from exact freezing in a high-frequency expansion.
Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization and growth of entanglement. The phenomenology of , whereby a translationally invariant many-body system exhibits emergent conservation laws and a slow growth of entanglement entropy at certain fixed ratios of a drive amplitude and frequency, presents a novel paradigm for retaining memory of an initial state up to late times. Previous studies of dynamical freezing have largely been restricted to a high-frequency Floquet-Magnus expansion and numerical exact diagonalization. Both techniques are unable to capture the slow approach to thermalization, or lack thereof, in a systematic fashion. By employing Floquet , where the time-dependent part of the Hamiltonian is gradually decoupled from the effective Hamiltonian using a sequence of unitary transformations, we unveil the universal approach to dynamical freezing and beyond, at asymptotically late times. We analyze the behavior associated with the flow renormalization at and near freezing using both exact-diagonalization and tensor-network-based methods and contrast the results with the conventional prethermal phenomenon. For a generic nonintegrable spin Hamiltonian with a periodic cosine wave drive, the flow approaches an unstable fixed point with an approximate emergent symmetry. We observe that at freezing the thermalization timescales are delayed compared to away from freezing, and the flow trajectory undergoes a series of events. Our numerical results are supported by analytical solutions to the flow equations.
Ergodic quantum many-body systems evolving under unitary time dynamics typically lose memory of their initial state via information scrambling. Here, we consider a paradigmatic translationally invariant many-body Hamiltonian of interacting bosons—a Josephson junction array in the transmon regime—in the presence of a strong Floquet drive. Generically, such a time-dependent drive is expected to heat the system to an effectively infinite-temperature, featureless state in the late-time limit. However, using numerical exact diagonalization, we find evidence of special ratios of the drive amplitude and frequency where the system develops emergent conservation laws and approximate integrability. Remarkably, at these same set of points, the Lyapunov exponent associated with the semi-classical dynamics for the coupled many-body equations of motion drops by at least an order of magnitude, arresting the growth of chaos. We supplement our numerical results with an analytical Floquet-Magnus expansion that includes higher-order corrections and capture the slow dynamics that control decay away from exact freezing.
A periodically driven quantum many-body system is believed to approach a locally infinite-temperature-like state as dictated by the ergodicity hypothesis, when all the couplings/parameters are of the same order. When the drive is stronger than a threshold value, a large class of systems is shown to break this mandate, exhibiting Dynamical Freezing (DF): ergodicity is broken due to the emergence of local operators with permanent memory of their initial values (PRX 11, 021008, 2021). However, an exception to DF has recently been noted in a particular setting (PRX 16, 011041, 2026). Here we identify the condition for ergodicity-breaking in a system under strong drive, and show how to stabilize DF by exact, local engineering. We further show that the Floquet Hamiltonian Heff=(i/T)ln[U(T)] is non-local when ordered by spin-flips, in a non-DF system, while it turns quasi-local under our simple, local DF engineering that keeps the Hamiltonian H(t) still non-integrable at each t. This perplexing non-universality is absent in equilibrium, where non-integrability is believed to imply ergodicity and thermalization universally. Our work paves a way to engineering novel ergodicity-broken interacting Floquet phases of matter in various quantum platforms, and also endows DF-assisted quantum error mitigation and state stabilization techniques (see Nature 653, 1027 (2026)) with unprecedented versatility and flexibility.
The ergodicity postulate, a foundational pillar of Gibbsian statistical mechanics predicts that a periodically driven (Floquet) system in the absence of any conservation law heats to a featureless `infinite temperature' state. Here, we find--for a clean and interacting generic spin chain subject to a {\it strong} driving field--that this can be prevented by the emergence of {\it approximate but stable} conservation-laws not present in the undriven system. We identify their origin: they do not necessarily owe their stability to familiar protections by symmetry, topology, disorder, or even high energy costs. We show numerically, {\it in the thermodynamic limit,} that when required by these emergent conservation-laws, the entanglement-entropy density of an infinite subsystem remains zero over our entire simulation time of several decades in natural units. We further provide a recipe for designing such conservation laws with high accuracy. Finally, we present an ensemble description, which we call the strongly driven ensemble incorporating these constraints. This provides a way to control many-body chaos through stable Floquet-engineering. Strong signatures of these conservation-laws should be experimentally accessible since they manifest in all length and time scales. Variants of the spin model we have used, have already been realized using Rydberg-dressed atoms.
Abstract Equilibrium statistical mechanics rests on the assumption of chaotic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs’ ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant conservation laws in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics of Floquet systems has a much richer structure due to the existence of emergent conservation laws: these are approximate but stable conservation laws arising due to the drive, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This indicates to the possibility of stable Floquet phases of matter in disorder-free systems. This review intends to give a self-contained theoretical overview of these developments for a broad physics audience. We conclude by briefly surveying the current experimental scenario.
Interacting many-body quantum systems are believed to heat up unboundedly under a periodic drive as there is no local conservation law to prevent this from happening. Here, the authors show that this belief may not be generally true. Their results indicate that under strong periodic driving quantum interference may suppress the heating and may lead to a nonthermal state, remembering properties of the initial state until infinite time. This is accounted for by the emergence of an approximately conserved local quantity. The freezing is more pronounced for smaller drive frequencies, putting it beyond the scope of conventionally used high-frequency expansions.