Many-body Scars Research Articles

Exact quantum scars in the chiral nonlinear Luttinger liquid

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit of an analytic solution. Nonetheless, the authors find a number of exact eigenstates for a large family of density-density interaction terms. These quantum many-body scar states are embedded in a continuum of strongly correlated excited states. They exhibit identically zero momentum-space entanglement. Among other properties, this sets them apart from many previous examples of quantum many-body scars.

Stability of scar states in the two-dimensional PXP model against random disorder

Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These systems feature a special band of eigenstates called quantum many-body scar states in the energy spectrum. In this work we study the fate of quantum many-body scar states in a two-dimensional lattice against random disorders. We show that in both the square lattice and the honeycomb lattice the scar states can persist up to a finite disorder strength, before eventually being erased by the disorder. We further study the localization properties of the system in the presence of even stronger disorders and show that whether a full localization transition occurs depends on the type of disorder we introduce. Our study thus reveals the fascinating interplay between disorder and quantum many-body scarring in a two-dimensional system.

Group theoretic approach to many-body scar states in fermionic lattice models

It has been shown [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that three families of highly symmetric states are many-body scars for any spin-$\frac{1}{2}$ fermionic Hamiltonian of the form ${H}_{0}+OT$, where $T$ is a generator of an appropriate Lie group. One of these families consists of the well-known $\ensuremath{\eta}$-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine tuning. The explicit ${H}_{0}+OT$ decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write all the generators $T$ that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the ``revivals.'' A full numerical study of an extended two-dimensional $tJU$ model explicitly illustrates the novel properties of the invariant scars and supports our findings.

Orthogonal Quantum Many-Body Scars.

Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.

Fate of Quantum Many-Body Scars in the Presence of Disorder

Experiments performed on strongly interacting Rydberg atoms have revealed surprising persistent oscillations of local observables. These oscillations have been attributed to a special set of non-ergodic states, referred to as quantum many-body scars. Although a significant amount of research has been invested to understand these special states, it has remained unclear how stable scar states are against disorder. We address this question by studying numerically and analytically the magnetization and spatio-temporal correlators of a model of interacting Rydberg atoms in the presence of disorder. While the oscillation amplitudes of these observables decay with time as the disorder strength is increased, their oscillation frequency remains remarkably constant. We show that this stability stems from resonances in the disordered spectrum that are approximately centered at the same scar energies of the clean system. We also find that multiple additional sets of scar resonances become accessible due to the presence of disorder and further enhance the oscillation amplitudes. Our results show the robustness of non-ergodic dynamics in scar systems, and opens the door to understanding the behavior of experimentally realistic systems.

Motif magnetism and quantum many-body scars

We generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite energy density eigenstates are thermal. However, some systems, such as many-body localized systems and systems with quantum many-body scars, violate ETH and have high-energy athermal eigenstates. In systems with scars, most eigenstates thermalize, but a few atypical scar states do not. Scar states can give rise to a periodic revival when time-evolving particular initial product states, which can be detected experimentally. Recently, a family of spin Hamiltonians was found with magnetically ordered 3-colored eigenstates that are quantum many-body scars [Lee et al. Phys. Rev. B 101, 241111(2020)]. These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet. In this work, we introduce a generalized family of $n$-colored Hamiltonians with "spiral colored" eigenstates made from $n$-spin motifs such as polygons or polyhedra. We show how these models can be realized in many different lattice geometries and provide numerical evidence that they can exhibit quantum many-body scars with periodic revivals that can be observed by time-evolving simple product states. The simple structure of these Hamiltonians makes them promising candidates for future experimental studies of quantum many-body scars.

Topological quantum many-body scars in quantum dimer models on the kagome lattice

We present a class of quantum dimer models on the kagome lattice with full translational invariance that feature a quantum many-body scar state of analytically known entanglement properties within their spectra. Using exact diagonalization on lattices of up to 60 sites, we show that non-scar states conform to the eigenstate thermalization hypothesis. Specifically, we show that energies are distributed according to the Gaussian ensemble expected of their respective symmetry sector, illustrate the existence of the scar from bipartite entanglement properties, and demonstrate revival phenomena in studies of fidelity dynamics.

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving.

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein etal. Science 371, 1355 (2021)SCIEAS0036-807510.1126/science.abg2530] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

Multiple quantum scar states and emergent slow thermalization in a flat-band system

Quantum many-body scars (QMBS) appear in a flat-band model with interactions on the saw-tooth lattice. The flat-band model includes a compact support localized eigenstates, called compact localized state (CLS). Some characteristic many-body states can be constructed from the CLSs at a low-filling on the flat-band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, these states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with sub-volume or area law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in non-integrable systems with the violation of the strong ETH and the QMBS.

Quantum scars and bulk coherence in a symmetry-protected topological phase

Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-$1/2$ chain with three-site "cluster" terms hosting a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase. Focusing on the weakly interacting regime, we find that eigenstates with volume-law entanglement coexist with area-law entangled eigenstates throughout the spectrum. We show that a subset of the latter can be constructed by virtue of repeated cluster excitations on the even or odd sublattice of the chain, resulting in an equidistant "tower" of states, analogous to the phenomenology of quantum many-body scars. We further demonstrate that these scarred eigenstates support nonthermal expectation values of local cluster operators in the bulk and exhibit signatures of topological order even at finite energy densities. Studying the dynamics for out-of-equilibrium states drawn from the noninteracting "cluster basis", we unveil that nonthermalizing bulk dynamics can be observed on long time scales if clusters on odd and even sites are energetically detuned. In this case, cluster excitations remain essentially confined to one of the two sublattices such that inhomogeneous cluster configurations cannot equilibrate and thermalization of the full system is impeded. Our work sheds light on the role of quantum many-body scars in preserving SPT order at finite temperature and the possibility of coherent bulk dynamics in models with SPT order beyond the existence of long-lived edge modes.

Hilbert space fragmentation and exact scars of generalized Fredkin spin chains

In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics by quenching different initial states that is shown through large scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays non-ergodic dynamics as a result of sharing the same fragmentation structure and scarring as the Hamiltonian.

Emergent symmetries and slow quantum dynamics in a Rydberg-atom chain with confinement

Rydberg atoms in optical tweezer arrays provide a playground for nonequilibrium quantum many-body physics. The PXP model describes the dynamics of such systems in the strongly interacting Rydberg blockade regime and notably exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we study the PXP model in a strong staggered external field, which has been proposed to manifest quasiparticle confinement in light of a mapping to a lattice gauge theory. We characterize this confining regime using both numerical exact diagonalization and perturbation theory around the strong-field limit. In addition to the expected emergent symmetry generated by the staggered field, we find a second emergent symmetry that is special to the PXP model. The interplay between these emergent symmetries and the Rydberg blockade constraint dramatically slows down the system's dynamics beyond naive expectations. We devise a nested Schrieffer-Wolff perturbation theory to properly account for the new emergent symmetry, and we show that this treatment is essential to understand the numerically observed relaxation time scales. We also discuss connections to Hilbert space fragmentation, and we trace the origin of the new emergent symmetry to a ``nearly-$\text{SU}(2)$'' algebra discovered in the context of many-body scarring.

Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory on Ladders.

We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.

Disorder enhanced quantum many-body scars in Hilbert hypercubes

We consider a model arising in facilitated Rydberg chains with positional disorder which features a Hilbert space with the topology of a $d$-dimensional hypercube. This allows for a straightforward interpretation of the many-body dynamics in terms of a single particle one on the Hilbert space and provides an explicit link between the many-body and single particle scars. Exploiting this perspective, we show that an integrability-breaking disorder enhances the scars followed by inhibition of the dynamics due to strong localization of the eigenstates in the large disorder limit. Next, mapping the model to the spin-1/2 XX Heisenberg chain offers a simple geometrical perspective on the recently proposed Onsager scars [PRL ${\bf 124}$, 180604 (2020)], which can be identified with the scars on the edge of the Hilbert space. This makes apparent the origin of their insensitivity to certain types of disorder perturbations.

Robust Quantum Sensing in Strongly Interacting Systems with Many-Body Scars

In most quantum sensing schemes, interactions between the constituent particles of the sensor are expected to lead to thermalisation and degraded sensitivity. However, recent theoretical and experimental work has shown that the phenomenon of quantum many-body scarring can slow down, or even prevent thermalisation. We show that scarring can be exploited for quantum sensing that is robust against certain strong interactions. In the ideal case of perfect scars with harmonic energy gaps, the optimal sensing time can diverge despite the strong interactions. We demonstrate the idea with two examples: a spin-1 model with Dzyaloshinskii-Moriya interaction, and a spin-1/2 mixed-field Ising model. We also briefly discuss some non-ideal perturbations, and the addition of periodic controls to suppress their effect on sensing.

Quantum many-body scars and weak breaking of ergodicity

Thermalization is the inevitable fate of many complex quantum systems, whose dynamics allow them to fully explore the vast configuration space regardless of the initial state—the behaviour known as quantum ergodicity. In a quest for experimental realizations of coherent long-time dynamics, efforts have focused on ergodicity-breaking mechanisms, such as integrability and localization. The recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of behaviour where the system rapidly relaxes for most initial conditions, while certain initial states give rise to non-ergodic dynamics. This collective effect has been named ‘quantum many-body scarring’ by analogy with a related form of weak ergodicity breaking that occurs for a single particle inside a stadium billiard potential. In this Review, we provide a pedagogical introduction to quantum many-body scars and highlight the emerging connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to embedded algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology.

Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model.

Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg etal., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime U≈Δ≫J at electronic filling factor ν=1. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realizations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the Fermi-Hubbard model is different from other examples in the literature: the scars originate from a subgraph, representing a free spin-1 paramagnet, which is weakly connected to the rest of the Hamiltonian's adjacency graph. Our work demonstrates that correlated fermions in tilted optical lattices provide a platform for understanding the interplay of many-body scarring and other forms of ergodicity breaking, such as localization and Hilbert space fragmentation.

Correspondence Principle for Many-Body Scars in Ultracold Rydberg Atoms

The theory of quantum scarring -- a remarkable violation of quantum unique ergodicity -- rests on two complementary pillars: the existence of unstable classical periodic orbits and the so-called quasimodes, i.e., the non-ergodic states that strongly overlap with a small number of the system's eigenstates. Recently, interest in quantum scars has been revived in a many-body setting of Rydberg atom chains. While previous theoretical works have identified periodic orbits for such systems using time-dependent variational principle (TDVP), the link between periodic orbits and quasimodes has been missing. Here we provide a conceptually simple analytic construction of quasimodes for the non-integrable Rydberg atom model, and prove that they arise from a "requantisation" of previously established periodic orbits when quantum fluctuations are restored to all orders. Our results shed light on the TDVP classical system simultaneously playing the role of both the mean-field approximation and the system's classical limit, thus allowing us to firm up the analogy between the eigenstate scarring in the Rydberg atom chains and the single-particle quantum systems.

Exact many-body scars and their stability in constrained quantum chains

Quantum scars are non-thermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states (MPS) with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to breakdown when all orders are taken into account. We further investigate models with larger blockade radius and find a novel set of exact quantum scars, that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.

Disorder-free localization and many-body quantum scars from magnetic frustration

The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars -- eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.