The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.
The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.
Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.
Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this paper, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasiperiodic Thue-Morse or a family of sequences with n -multipolar temporal correlations. We demonstrate that multiple heating channels can be eliminated . The number of eliminated channels increases with multipolar order n . We illustrate this in a classical kicked rotor chain where we find a long-lived prethermal regime. When the static Hamiltonian only involves the kinetic energy, the prethermal lifetime t* can strongly depend on the temporal correlations of the drive, with a power-law dependence on the t*∼K−2n , for which we can account using a simple linearization argument. Published by the American Physical Society 2024
We establish some general dynamical properties of quantum many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasiconserved extensive quantity H∗, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well approximated by the evolution with the Hamiltonian H∗ up to time ${\ensuremath{\tau}}_{*}$, which is exponentially large in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where H∗ is ergodic, the driven system prethermalizes to a thermal state described by H∗ at intermediate times $t\ensuremath{\lesssim}{\ensuremath{\tau}}_{*}$, eventually heating up to an infinite-temperature state after times $t\ensuremath{\sim}{\ensuremath{\tau}}_{*}$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.
Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives. We demonstrate that the thermalization time scales as (1/T)^{2n+2}, where n is the multipolar order and T is the intrinsic time-scale associated with the drive. In the n→∞ limit, the drive becomes quasiperiodic and the thermalization time becomes exponentially long [∼exp(β/T)]. We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals.
Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n+1. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges.
Time-dependent drives hold promise for realizing non-equilibrium many-body phenomena that are absent in undriven systems1–3. Yet, drive-induced heating normally destabilizes the systems4,5, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives6,7. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Here, using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other way by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n + 1. Using quantum-state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a two-dimensional configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges. The existence of a long-lived, prethermal regime in many-body systems with tunable heating rates, driven by structured random protocols, is observed using a 78-qubit superconducting quantum processor.