Time-periodic driving provides a promising route toward engineering nontrivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable, noninteracting systems can synchronize with the driving into a nontrivial periodic motion, generic nonintegrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasiperiodic time evolution over many periods can also emerge in weakly interacting systems, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analog of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.
Time-periodic driving provides a promising route toward engineering nontrivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable, noninteracting systems can synchronize with the driving into a nontrivial periodic motion, generic nonintegrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasiperiodic time evolution over many periods can also emerge in weakly interacting systems, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analog of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.
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.
Exploiting the rich phenomenology of periodically driven many-body systems is notoriously hindered by persistent heating in both the classical and the quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilization of a nontrivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and we simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite frequency and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a global synchronized Gibbs state emerges, whose temperature may depart significantly from the initial temperature of the reservoir. Although our analysis in some parts relies on the specific properties of our setup, we argue that much of its phenomenology could be generic.
We study the dynamics of the Fermi-Hubbard model driven by a time-periodic modulation of the interaction within nonequilibrium dynamical mean-field theory. For moderate interaction, we find clear evidence of thermalization to a genuine infinite-temperature state with no residual oscillations. Quite differently, in the strongly correlated regime, we find a quasistationary extremely long-lived state with oscillations synchronized with the drive (Floquet prethermalization). Remarkably, the nature of this state dramatically changes upon tuning the drive frequency. In particular, we show the existence of a critical frequency at which the system rapidly thermalizes despite the large interaction. We characterize this resonant thermalization and provide an analytical understanding in terms of a breakdown of the periodic Schrieffer-Wolff transformation.
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.
While a clean, driven system generically absorbs energy until it reaches "infinite temperature," it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethernial regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.
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.