The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite-energy density, leads to an absence of ergodicity and long-time coherent dynamics starting from initial states that have a high overlap with scars as experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and weak ergodicity breaking regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the Floquet spectrum of the system. The latter regime, in contrast, has scars; they lead to long-time coherent dynamics of correlation functions. We provide an analytical explanation of the existence of these regimes by going beyond a high-frequency Magnus expansion and using a novel perturbative approach valid at large drive amplitudes to derive a Floquet Hamiltonian which qualitatively explains the behavior of the driven system at arbitrary frequencies. We also discuss experiments involving finite Rydberg chains which can validate our theory. Our results demonstrate the possibility of drive-frequency-induced tuning between ergodic and weak ergodicity breaking dynamics in a disorder-free quantum many-body system.
The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite-energy density, leads to an absence of ergodicity and long-time coherent dynamics starting from initial states that have a high overlap with scars as experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and weak ergodicity breaking regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the Floquet spectrum of the system. The latter regime, in contrast, has scars; they lead to long-time coherent dynamics of correlation functions. We provide an analytical explanation of the existence of these regimes by going beyond a high-frequency Magnus expansion and using a novel perturbative approach valid at large drive amplitudes to derive a Floquet Hamiltonian which qualitatively explains the behavior of the driven system at arbitrary frequencies. We also discuss experiments involving finite Rydberg chains which can validate our theory. Our results demonstrate the possibility of drive-frequency-induced tuning between ergodic and weak ergodicity breaking dynamics in a disorder-free quantum many-body system.
We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.
The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians.Our model is based on the PXP-type interactions without disorder.We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions.This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis.Through the exact expression of the scar states, the underlying physical mechanism is clarified.Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.
We study the dynamics of a periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0\ensuremath{\rangle}$) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes $(L\ensuremath{\le}26)$, that the Floquet Hamiltonian of the system, within a range of drive frequencies that we chart out, hosts a set of quantum scars that have large overlap with the $|0\ensuremath{\rangle}$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state $(|{\mathbb{Z}}_{2}\ensuremath{\rangle})$; they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0\ensuremath{\rangle}$ state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing, and we provide an analytic explanation for this phenomenon. Finally, we demonstrate that for a wide range of drive frequencies, the system reaches a steady state with subthermal values of the density-density correlator. The presence of such subthermal steady states, which are absent for dynamics starting from the $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$ state, imply a weak violation of the eigenstate thermalization hypothesis in finite-sized Rydberg chains distinct from that due to the scar-induced persistent oscillations reported earlier. We conjecture that in the thermodynamic limit, such states may exist as prethermal steady states that show anomalously slow relaxation. We supplement our numerical results by deriving an analytic expression for the Floquet Hamiltonian using a Floquet perturbation theory in the high amplitude limit, which provides an analytic, albeit qualitative, understanding of these phenomena at arbitrary drive frequencies. We discuss experiments that can test our theory.
The success of statistical mechanics in describing complex quantum systems rests upon typicality properties such as ergodicity. Both integrable systems and the recently discovered many-body localisation show that these assumptions can be strongly violated in either finely tuned cases, or in the presence of quenched disorder. In this thesis, we uncover a qualitatively different form of ergodicity breaking, wherein a small number of atypical eigenstates are embedded throughout an otherwise thermalising spectrum. We call this a many-body quantum scar, in analogy to quantum scars in single-particle quantum chaos, where quantum scarred eigenfunctions concentrate around associated periodic classical trajectories. \nWe demonstrate that many-body quantum scars can be found in an unusual model recently realised in a 51 Rydberg atom quantum simulator. The observed coherent oscillations following in a certain quench experiment are a consequence of the quantum scar. At the same time, the level statistics rules out conventional explanations such as integrability and many-body localisation. We develop an approximate method to construct scarred eigenstates, in order to describe their structure and physical properties. Additionally, we find a local perturbation which makes these non-equilibrium properties much more pronounced, with near perfect quantum revivals. At the same time the other eigenstates remain thermal. Our results suggest that many-body quantum scars forms a new class of quantum dynamics with unusual properties, which are realisable in current experiments.
We study the stroboscopic dynamics of a periodically driven finite Rydberg chain with staggered ($\mathrm{\ensuremath{\Delta}}$) and time-dependent uniform $[\ensuremath{\lambda}(t)]$ detuning terms using exact diagonalization. We show that at intermediate drive frequencies (${\ensuremath{\omega}}_{D}$), the presence of a finite $\mathrm{\ensuremath{\Delta}}$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. Such clustering is lost at special commensurate drive frequencies for which $\ensuremath{\hbar}{\ensuremath{\omega}}_{d}=n\mathrm{\ensuremath{\Delta}}$ ($n\ensuremath{\in}Z$) leading to restoration of ergodicity. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density-density correlation between Rydberg excitations at even sites of the chain for specific ${\ensuremath{\omega}}_{D}$. Such a correlator exhibits stable oscillations with perfect revivals when driven close to the freezing frequencies for initial all spin-down ($|0\ensuremath{\rangle}$) or Neel ($|{\mathbb{Z}}_{2}\ensuremath{\rangle}$, with up spins on even sites) states. In contrast, for the $|{\overline{\mathbb{Z}}}_{2}\ensuremath{\rangle}$ (time-reversed partner of $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$) initial state, we find complete absence of such oscillations leading to freezing for a range of ${\ensuremath{\omega}}_{D}$; this range increases with $\mathrm{\ensuremath{\Delta}}$. We also study the properties of quantum many-body scars in the Floquet spectrum of the model as a function of $\mathrm{\ensuremath{\Delta}}$ and show the existence of mid-spectrum scars at large $\mathrm{\ensuremath{\Delta}}$ which do not have overlap with either $|0\ensuremath{\rangle}$ or $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$ states. We supplement our numerical results with those from an analytic Floquet Hamiltonian computed using Floquet perturbation theory which allows us to provide qualitative analytical explanations of the above-mentioned numerical results.
Unstable periodic orbits act as organizing structures for classical chaotic systems and underpin quantum scarring. Long known in single-particle systems, genuine quantum scars based on unstable periodic orbits have been recently extended to isolated many-body systems for time-independent Hamiltonians. Their fate under periodic driving, however, remains largely uncharted, challenged by the expectation that these systems should in general heat to infinite temperature. Here, we investigate how genuine scarring competes with the drive in a Floquet many-body system. Using chaotic spin chains, we demonstrate that Floquet states remain scarred in the high-frequency limit. Beyond this static correspondence, we uncover additional, driving-induced Floquet scars with no static analog. We construct a rich dynamical stability diagram with intermediate-frequency regimes of enhanced and quenched scarring, which we understand with a classical analysis of the Lyapunov exponent. Our results position Floquet systems as a natural platform for tuning the scarring behavior of quantum many-body systems.