Many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS) are well-established mechanisms of ergodicity breaking in quantum systems. Recently, asymptotic quantum many-body scars (AQMBS), non-thermal states whose stability grows with system size, have been proposed theoretically and probed experimentally. Here, we show that AQMBS arise naturally as remnants of certain quantum phase transitions. For a broad class of frustration-free Hamiltonians, we prove that their gapless excitations survive deformation into a scarred Hamiltonian as states whose energy variance is bounded by the excitation gap. Consequently, the gapless excitations at a quantum critical point become AQMBS of the scarred Hamiltonian. Their fidelity relaxation time is then set by the critical scaling of the gap, determined by the dynamic critical exponent. Modelling the critical Fredkin and Motzkin chains and the two-dimensional PVBS model, we obtain AQMBS whose variances directly reflect the dynamic exponents of the underlying transitions. Where the gap of the Motzkin chain closes super-exponentially, we find exponentially stable AQMBS, for which we also observe numerical evidence of volume-law entanglement.
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Many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS) are well-established mechanisms of ergodicity breaking in quantum systems. Recently, asymptotic quantum many-body scars (AQMBS), non-thermal states whose stability grows with system size, have been proposed theoretically and probed experimentally. Here, we show that AQMBS arise naturally as remnants of certain quantum phase transitions. For a broad class of frustration-free Hamiltonians, we prove that their gapless excitations survive deformation into a scarred Hamiltonian as states whose energy variance is bounded by the excitation gap. Consequently, the gapless excitations at a quantum critical point become AQMBS of the scarred Hamiltonian. Their fidelity relaxation time is then set by the critical scaling of the gap, determined by the dynamic critical exponent. Modelling the critical Fredkin and Motzkin chains and the two-dimensional PVBS model, we obtain AQMBS whose variances directly reflect the dynamic exponents of the underlying transitions. Where the gap of the Motzkin chain closes super-exponentially, we find exponentially stable AQMBS, for which we also observe numerical evidence of volume-law entanglement.
One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic quantum matter, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations and AQMBS in certain qudit-based models. We then consider a 2-local model, hosting both conventional and asymptotic scars, in which the AQMBS states are gapless excitations of a ground state localisation transition. By exploiting the structure of the found AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation behaviour under Floquet dynamics. Performing simulations on up to N = 20 qubits and up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing the first experimental signatures of asymptotic scars.
A generic closed quantum many-body system will inevitably tend to thermalization, whose local information encoded in the initial state eventually scrambles into the full space, known as quantum ergodicity. A paradigmatic exception in closed quantum systems for strong ergodicity breaking is known as many-body localization, where strong disorder-induced localization prevents the occurrence of thermalization. It is generally recognized that a localized quantum system would be delocalized under dissipation induced by the environment. However, this consequence recently has received challenges where an exotic dissipation-induced localization mechanism is proposed, and transitions between localized and extended phases are found. In this Letter, we promote this mechanism to systems for weak ergodicity breaking hosting quantum many-body scars (QMBS). We find that the system relaxes to a steady state dominated by QMBS, and the dissipative dynamics exhibit dynamic revivals by suitably preparing an initial state. We point out an experimental realization of the controlled dissipation with a cold atomic setup. This makes the signature of ergodicity breaking visible over dissipative dynamics and offers potential possibilities for experimentally preparing stable QMBS with associated coherent dynamics.
We consider a quantum lattice spin model featuring exact quasiparticle towers of eigenstates with low entanglement at finite size, known as quantum many-body scars (QMBS). We show that the states in the neighboring part of the energy spectrum can be superposed to construct entire families of low-entanglement states whose energy variance decreases asymptotically to zero as the lattice size is increased. As a consequence, they have a relaxation time that diverges in the thermodynamic limit, and therefore exhibit the typical behavior of exact QMBS, although they are not exact eigenstates of the Hamiltonian for any finite size. We refer to such states as asymptotic QMBS. These states are orthogonal to any exact QMBS at any finite size, and their existence shows that the presence of an exact QMBS leaves important signatures of nonthermalness in the rest of the spectrum; therefore, QMBS-like phenomena can hide in what is typically considered the thermal part of the spectrum. We support our study using numerical simulations in the spin-1 XY model, a paradigmatic model for QMBS, and we conclude by presenting a weak perturbation of the model that destroys the exact QMBS while keeping the asymptotic QMBS.
This thesis investigates the anomalous dynamics observed in a Rydberg atom experiment in the broadest sense: a strongly interacting spin chain, without integrability or disorder, exhibits coherent many-body revivals ensuing only from specific initial states. This non-thermal behavior is attributed to the presence of quantum many-body scars (QMBS), a novel class of ergodicity breaking phenomena. Unlike other non-thermalizing systems such as integrable models and many-body localization, the mechanism of ergodicity breaking in QMBS is quite subtle, relying on a (vanishingly) small subset of anomalous eigenstates, known as scar states: one could observe ergodicity breaking only if initial states have appreciable overlap with these scar states. In other words, systems hosting QMBS are indistinguishable from typical chaotic, thermalizing systems, except for scar states. While the theoretical understanding of QMBS has advanced through the investigation of various toy quantum models, ranging from the Affleck-Kennedy-Lieb-Tasaki (AKLT) model to the Hubbard model, these insights do not fully resolve the mysterious oscillations in the Rydberg experiment: crucially the wavefunction corresponding to the experiment, and its relation to many other toy models in the literature remain open questions. Furthermore, beyond mathematical curiocity, the observability of non-thermal dynamics suggests that QMBS may yield distinct physical effects. the nature of which remains to be determined. This dissertation addresses these issues by solving two concrete problems: (i) the mathematical characterization of scar states in the PXP model, the effective model for the experiment, and (ii) the identification of physical consequences of QMBS in both short- and long-time dynamics. In the first part, we clarify the algebraic structure underlying the scar states of the PXP model and derive analytic ansatz for these wavefunctions. The proposed forms make explicit the hidden algebraic structure of the PXP scars and demonstrate how this structure is shared with many other QMBS Hamiltonians, including the AKLT model. The second part investigates dynamical signatures and robustness. Given the fragility of many-body eigenstates to perturbations, identifying which scar characteristics survive realistic perturbations is crucial. In closed systems, we show that out-of-time-ordered correlators (OTOCs) and the associated Lyapunov exponent can distinguish QMBS from generic chaotic states, at least within a semiclassical regime. Specifically, the OTOC growth associated with scar states is parametrically slower and remains slow under small ``scar-breaking'' perturbations. For open systems governed by non-Hermitian dynamics, we introduce a novel non-equilibrium phase, the QMBS phase, where the long-time wavefunction is localized in a small corner of the Hilbert space. We further identify a first-order transition between the QMBS phase and a thermal phase, where the wavefunction becomes delocalized.
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.
Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare ``scarred'' eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is subextensive. When internal symmetries are present, the construction leads to multiple, and even towers, of rainbow scars revealed through distinctive non-thermal dynamics. Remarkably, certain symmetries can lead rainbow scars to arise in translation-invariant models. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system.