The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.
The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.
The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.
Unstable periodic orbits (UPOs) play a key role in the theory of chaos, constituting the ``skeleton'' of classical chaotic systems and ``scarring'' the eigenstates of the corresponding quantum system. Recently, nonthermal many-body eigenstates embedded in an otherwise thermal spectrum have been identified as a many-body generalization of quantum scars. The latter, however, are not clearly associated to a chaotic phase space, and the connection between the single- and many-body notions of quantum scars remains therefore incomplete. Here, we find the first quantum many-body scars originating from UPOs of a chaotic phase space. Remarkably, these states verify the eigenstate thermalization hypothesis, and we thus refer to them as thermal quantum many-body scars. While they do not preclude thermalization, their spectral structure featuring approximately equispaced towers of states yields an anomalous oscillatory dynamics preceding thermalization for wavepackets initialized on an UPO. Remarkably, our model hosts both types of scars, thermal and nonthermal, and allows us to study the crossover between the two. Our work illustrates the fundamental principle of classical-quantum correspondence in a many-body system and its limitations.
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.
Quantum many-body scars consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of quantum many-body scars follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit. A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the eigenstate thermalization hypothesis, and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical unstable periodic orbits, while satisfying the eigenstate thermalization hypothesis. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates.
To probe the limits of dynamic thermalization, we numerically investigate the stability of exceptional periodic classical trajectories in chaotic many-spin systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates known as "quantum many-body scars." The systems considered are chaotic spin chains with short-range interactions, both classical and quantum. On the classical side, the chosen periodic trajectories are such that all spins instantaneously point in the same direction, which evolves as a function of time. We find that the largest Lyapunov exponents characterizing the stability of these trajectories have surprisingly strong and nontrivial dependencies on the interaction constants and chain lengths. In particular, we identify rather long spin chains, where the above periodic trajectories are Lyapunov stable on many-body energy shells overwhelmingly dominated by chaotic motion. We show that the above phenomenology can be quantitatively described by connecting Lyapunov instabilities of translationally invariant periodic trajectories to irreducible representations of the translational symmetry group with well-defined wave vectors. We also find that instabilities around periodic trajectories in modestly large spin chains develop into a transient nearly quasiperiodic nonergodic regime. In some cases, the lifetime of this regime is extremely long, which we interpret as a manifestation of Arnold diffusion in the vicinity of integrable dynamics. On the quantum side, we numerically investigate the dynamics of quantum states starting with all spins initially pointing in the same direction: These are the quantum counterparts of the initial conditions for the above periodic classical trajectories. Our investigation reveals the existence of quantum many-body scars for numerically accessible finite chains of spins-3/2 and higher. No evidence of quantum scars was observed for spin-1/2 chains, while spin-1 chains were found to be transitional in this respect. The dynamic thermalization process dominated by quantum scars is shown to exhibit a slowdown in comparison with generic thermalization at the same energy. Finally, we identify quantum signatures of the proximity to a classical separatrix of the periodic motion.
Quantum many-body scars (QMBSs) represent a weak ergodicity-breaking phenomenon that defies the common scenario of thermalization in closed quantum systems. They are often regarded as a many-body analog of quantum scars (QSs)—a single-particle phenomenon in quantum chaos—due to their superficial similarities. However, unlike QSs, a clear connection between QMBSs and classical chaos has remained elusive. It has nevertheless been speculated that in an appropriate semiclassical limit, QMBSs should have a correspondence to weakly unstable periodic orbits. In this paper, I present a counterexample to this conjecture by studying a bosonic model with a large number of flavors. The dynamics of out-of-time-ordered correlators (OTOCs) suggest that QMBS do not display chaotic behavior in the semiclassical limit. In contrast, chaotic dynamics are expected for initial states not associated with QMBS. Interestingly, the anomalous OTOC dynamics persist even under weak perturbations that eliminate the scarred eigenstates, suggesting a certain robustness in the phenomenon.