We study the paradigmatic spin-1 XY chain under open boundary conditions, which hosts exact quantum many-body scars generated by an emergent Spectrum Generating Algebra (SGA). We show that the scar subspace possesses a symmetry-protected trivial (SPt) character that we attribute to a hidden $Z_{2}\times Z_{2}$ symmetry of another model, namely the commutant Hamiltonian, for which the scars are the ground states. We construct a Lieb-Schultz-Mattis (LSM) type twist operator, which, for scar states, takes the value $-1,$ and, for ergodic states, approaches zero in the thermodynamic limit. A complementary understanding of the stability of the scars under different perturbations is obtained by analyzing the Loschmidt echo and Quantum Fisher Information (QFI) of the scars. Finite-size scaling analysis of the QFI reveals that the scars are much more sensitive to perturbations as compared to the nearby thermal states. Based on the analysis of QFI and different LSM twist operators, we obtain a classification of different SGA-preserving and SGA-breaking perturbations.
Quantum scars correspond to enhanced probability densities along unstable classical periodic orbits. In recent years, research on quantum scars has extended to various systems including the many-body regime. In this work we focus on the formation, prevalence, and stability of linear "bouncing-ball" (BB) scars in two-dimensional (2D) quantum wells. These scars have relevance as effective and controllable channels in quantum transport. We utilize imaginary time propagation to solve the 2D Schrödinger equation within an arbitrary external confining potential, specifically the quantum well model with external perturbations. We show how BB scars begin to emerge with a single perturbative peak, such as a repulsive bump or attractive dip that simulates the effect of a charged nanotip in the system. We then identify the optimal size of the perturbative peak to maximize the prevalence of these scars. Finally, we investigate the stability of BB scars against external noise and find that some of them are remarkably robust. This suggests promising opportunities for further applications of BB scars in quantum transport.
Quantum many-body scars have received much recent attention for being both intriguing non-ergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with $N$ fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify $N/2+1$ scars for complex fermions due to the $U(1)$ symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin
We report the observation of unconventional transport phenomena in a spin-1 model that supports a tower of quantum many-body scars, and we discuss their properties uncovering their peculiar nature. In quantum many-body systems, the late-time dynamics of local observables are typically governed by conserved operators with local densities, such as energy and magnetization. In the model under investigation, however, there is an additional dynamical symmetry restricted to the subspace of the Hilbert space spanned by the quantum many-body scars. The latter significantly slows the decay of autocorrelation functions of certain coherent states of quantum many-body scars and is responsible for the unconventional form of transport that we detect numerically. We show that excited states with energy close to that of the quantum many-body scars play a crucial role in sustaining the transport. Finally, we propose a generalized eigenstate thermalization hypothesis to describe specific properties of states with energy close to the scars.
Quantum many-body scars are atypical nonthermal states embedded in the chaotic spectrum that evade conventional ergodicity. We propose the asymptotically AdS mini-boson star as a holographic candidate for scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The whole holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes a near-integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dynamics. These spectral, entanglement, and dynamical diagnostics provide unified evidence for holographic quantum scars in a self-gravitating system. Our work suggests a new connection between many-body scar physics, quantum chaos, and horizonless gravitational dynamics.
Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits (POs). First predicted 40 years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems whose classical counterpart is chaotic. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field. Here we demonstrate that, by using an in-situ graphene quantum dot (GQD) creation and wavefunction mapping technique, quantum scars are imaged for Dirac electrons with nanometer spatial resolution and meV energy resolution with a scanning tunneling microscope. Specifically, we find enhanced probability densities in the form of lemniscate-shaped and streak-like patterns within our stadium-shaped GQDs. Both features show equal energy interval recurrence, consistent with predictions for relativistic quantum scars. By combining classical and quantum simulations, we demonstrate that the observed patterns correspond to two unstable POs that exist in our stadium-shaped GQD, thus proving they are both quantum scars. In addition to providing the first unequivocal visual evidence of quantum scarring, our
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 in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to nonthermal dynamics. We introduce a graph-theoretic framework to find suitable candidates for scarring on arbitrary lattices. Our framework predicts two distinct mechanisms: type-I scars generalize the bipartite case by using locally entangled states to overcome mild frustration, while type-II scars exploit strong frustration to pin part of the lattice, leaving the remainder to oscillate freely. We numerically demonstrate both mechanisms and uncover an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization. Our results establish scarring as a generic feature of Rydberg systems beyond one dimension and provide an experimentally accessible route to systematically probing non-thermal dynamics in quantum simulators.
Quantum many-body scars are energy eigenstates which fail to reproduce thermal expectation values of local observables, in systems where the rest of the many-body spectrum fulfils eigenstate thermalization. Experimental observation of quantum many-body scars has so far been limited to models with multiple scar states evenly spaced in energy. It is thus an interesting question whether even single isolated scars, which theoretically embody the weakest possibile violation of eigenstate thermalization and may be thought to have no detectable impact in experiments, can leave a trace in measurable quantities. Moreover, single scars offer an interesting scenario for exploring the connection between quantum many-body scars and the original notion of scarring in quantum dynamical systems theory. Here we propose protocols to observe single scars in architectures of fixed-frequency, fixed-coupling superconducting qubits. We first adapt known models possessing the desired features into a form particularly suited for the experimental platform. We develop protocols for the implementation of these models, through trotterized sequences of two-qubit cross-resonance interactions, and verify the exis
We show that the spin-s square-lattice Heisenberg model has exact many-body scars. These scars are simple valence-bond solids with exactly zero energy, and they exist in even-by-even systems and ladders of width 2. Ladders have additional scars corresponding to injecting one or two magnons on top of a parent valence-bond solid scar. These scars have a remarkably simple physical origin based only the angular momentum algebra and cancellations from spin-antialignment within a valence bond. Our comprehensive exact diagonalization calculations suggest that our valence-bond solids exhaust all exact eigenstates in the Heisenberg model except for few-magnon states near the top of the spectrum. Our scars are interesting because they are not part of a tower, have area-law entanglement, break translation symmetry, and exist for Heisenberg models of all spin.
The recent observations of persistent revivals in the Rydberg atom chain have revealed a weak ergodicity breaking mechanism known as quantum many-body scars, which is typically a collection of states with low entanglement embedded in otherwise thermal spectra. Here, by generalizing a generic formalism, we propose a direct evolution from the quantum many-body scars to the multiple inverted quantum many-body scars, i.e., different sets of excited states with volume-law entanglement embedded in a sea of the many-body localized spectrum. When increasing the disorder strength, a tower of exact eigenstates remain intact, acting as conventional quantum many-body scars at weak disorder, and each residing inside narrow energy windows with the emerged inverted quantum many-body scar at strong disorder. Moreover, the strong disorder also induces additional sets of inverted quantum many-body scars with their energies concentrating in the middle of the exact eigenstates. As a result, all the multiple inverted quantum many-body scars are approximately equidistant in energy. We further examine the stability of the conventional and the inverted quantum many-body scars against the external random f
Quantum many-body scars break ergodicity and evade thermalization, resulting in sub-volume law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy in the thermodynamic limit. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occu
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 to study the crossover between the two. Our work illustrates the fundamental principle of classical-quantum correspondence in
We study the stability of the many-body scars in spin-1/2 fermionic systems under the most typical perturbations in relevant materials. We find that some families of scars are completely insensitive to certain perturbations. In some other cases they are stable to the first order in perturbation theory. Our analytical results apply to a large class of Hamiltonians that are known [arXiv:2106.10300] to support exact many-body scars. For the numerical calculations we choose the deformed $t-J-U$ model that includes both Heisenberg and Hubbard interactions. We propose two new stability measures that are based on physical observables rather than the fidelity to the exact initial wavefunction. They enable the experimental detection of scars and are more reliable from the theoretical and numerical perspectives. One of these measures may potentially find applications in other systems where the exact many-body scars are equally spaced in energy. In small systems and at small perturbations, a regime particularly relevant for quantum simulators, we identify and describe an additional stability exhibited by the many-body scars. For larger perturbation strengths we observe a distinct mode of ergo
We investigate the stability of quantum many-body scars under perturbations, within the PXP model. We numerically compute the fidelity and average correlations to monitor the state evolution and to identify revivals. The results indicate that, on the one hand, the entanglement entropy of PXP scars exhibit great sensitivity, in the sense that their profile approaches the ones expected for thermal states already for very small perturbations. On the other hand, other scar signatures, such as the revivals of states having large overlap with scars, show remarkable robustness. Additionally, we examined the effects of minor disturbances on initial states that previously exhibited high overlap with scars and consistent revivals. Our analysis revealed that different types of disturbances can induce markedly different behaviors, such as partially "freezing" the chain, leading to sustained oscillations, or accelerating the process of thermalization.
We introduce the concept of ergodicity and explore its deviation caused by quantum scars in an isolated quantum system, employing a pedagogical approach based on a toy model. Quantum scars, originally identified as traces of classically unstable orbits in certain wavefunctions of chaotic systems, have recently regained interest for their role in non-ergodic dynamics, as they retain memory of their initial states. We elucidate these features of quantum scars within the same framework of this toy model. The integrable part of the model consists of two large spins, with a classical counterpart, which we combine with a random matrix to induce ergodic behavior. Scarred states can be selectively generated from the integrable spin Hamiltonian by protecting them from the ergodic states using a projector method. Deformed projectors mimic the `quantum leakage' of scarred states, enabling tunable mixing with ergodic states and thereby controlling the degree of scarring. In this simple model, we investigate various properties of quantum scarring and shed light on different aspects of many-body quantum scars observed in more complex quantum systems. Notably, the underlying classicality can be r
Quantum scars are special eigenstates of many-body systems that evade thermalization. They were first discovered in the PXP model, a well-known effective description of Rydberg atom arrays. Despite significant theoretical efforts, the fundamental origin of PXP scars remains elusive. By investigating the discretized dynamics of the PXP model as a function of the Trotter step $τ$, we uncover a remarkable correspondence between the zero- and two-particle eigenstates of the integrable Floquet-PXP cellular automaton at $τ=π/2$ and the PXP many-body scars of the time-continuous limit. Specifically, we demonstrate that PXP scars are adiabatically connected to the eigenstates of the $τ=π/2$ Floquet operator. Building on this result, we propose a protocol for achieving high-fidelity preparation of PXP scars in Rydberg atom experiments.
Quantum scars are nonthermal eigenstates that prevent thermalization of initial states with weight on the scars. When the scar states are equally spaced in energy, superpositions of scars show oscillating local observables that can be detected in experiments. However, we note that scarred models in the literature show fundamentally different scar entanglement dynamics: some show entanglement oscillations while others are completely frozen. We explain this freezing through a no-go theorem which we apply to more than a dozen scarred models in the literature. We also discuss a method for evading the no-go theorem by deforming the scarred models with frozen scar entanglement dynamics.
We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call "statistical", and we identify specific signatures of the localized nature of these eigenstates by analyzing a combination of indicators of quantum ergodicity and properties related to the network structure of the model. Within this parallelism, we associate the emergence of statistical scars to the presence of "motifs" in the network, that reflects how these are associated to links with anomalously small connectivity. Most remarkably, statistical scars appear at well-defined values of energy, predicted solely on the base of network theory. We study the scaling of the number of statistical scars with system size: by continuously changing the connectivity of the system we find that there is a transition from a regime where the constraints are too weak for scars to exist for large systems to a regime where constraints are stronger and the number of statistical scars increases with system size. We estimate the location of this transition and we find that our e
Quantum many-body scars represent a form of weak ergodicity breaking that highlights the unusual physics of thermalization in quantum systems. Understanding scar formation promises insight into the connection between classical statistical mechanics and the quantum world. The existence of quantum many-body scars calls into question how the macroscopic world can arise from the Schrodinger equation. In this work, we demonstrate the existence of quantum many-body scars in the density-difference-dependent Hamiltonian. This Hamiltonian has a particular manifestation of chiral symmetry due to its interaction being neither attractive nor repulsive a prior, but depending on the configuration. As a result of this symmetry and peculiar interaction, we find that this system hosts two different classes of quantum scars; a charge density wave ordered scar and an edge-mode scar. We establish the existence of these scars by examining the entanglement entropy of the system as well as demonstrating robust thermalization breaking time dynamics. For each, we propose simple mechanisms that give rise to these scars which may be applicable to other systems.