Emerging quantum technologies hold the promise of unravelling difficult problems ranging from condensed matter to high-energy physics while, at the same time, motivating the search for unprecedented phenomena in their setting. Here, we use a custom-built superconducting qubit ladder to realize non-thermalizing states with rich entanglement structures in the middle of the energy spectrum. Despite effectively forming an "infinite" temperature ensemble, these states robustly encode quantum information far from equilibrium, as we demonstrate by measuring the fidelity and entanglement entropy in the quench dynamics of the ladder. Our approach harnesses the recently proposed type of non-ergodic behavior known as "rainbow scar," which allows us to obtain analytically exact eigenfunctions whose ergodicity-breaking properties can be conveniently controlled by randomizing the couplings of the model without affecting their energy. The on-demand tunability of quantum correlations via disorder allows for in situ control over ergodicity breaking, and it provides a knob for designing exotic many-body states that defy thermalization.
Emerging quantum technologies hold the promise of unravelling difficult problems ranging from condensed matter to high-energy physics while, at the same time, motivating the search for unprecedented phenomena in their setting. Here, we use a custom-built superconducting qubit ladder to realize non-thermalizing states with rich entanglement structures in the middle of the energy spectrum. Despite effectively forming an "infinite" temperature ensemble, these states robustly encode quantum information far from equilibrium, as we demonstrate by measuring the fidelity and entanglement entropy in the quench dynamics of the ladder. Our approach harnesses the recently proposed type of non-ergodic behavior known as "rainbow scar," which allows us to obtain analytically exact eigenfunctions whose ergodicity-breaking properties can be conveniently controlled by randomizing the couplings of the model without affecting their energy. The on-demand tunability of quantum correlations via disorder allows for in situ control over ergodicity breaking, and it provides a knob for designing exotic many-body states that defy thermalization.
Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.
Unraveling the mechanisms of ergodicity breaking in complex quantum systems is a central pursuit in nonequilibrium physics. In this work, we investigate a one-dimensional spin model featuring a tunable long-range hopping term, Hn, which introduces nonlocal interactions and bridges the gap between Hermitian and non-Hermitian regimes. Through a systematic analysis of level-spacing statistics, Krylov complexity, and entanglement entropy, we demonstrate that Hn acts as a universal control parameter driving the transition from integrability to quantum chaos. Specifically, increasing the strength of Hn induces a crossover from Poissonian to Gaussian Orthogonal Ensemble statistics in the Hermitian limit, and similarly triggers chaotic dynamics in the non-Hermitian case. Most remarkably, despite the onset of global chaos, we identify a tower of exact nonthermal eigenstates that evade thermalization. These states survive as robust quantum many-body scars, retaining low entanglement and coherent dynamics even under strong non-Hermitian perturbations. Our findings reveal a universal mechanism by which long-range and non-Hermitian effects reshape quantum ergodicity, offering new pathways for preserving quantum coherence in complex many-body systems.
The 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 applying a generic formalism, we reveal 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 entropy embedded in a sea of states with area-law entanglement. When increasing the disorder strength, a series of exact eigenstates, acting as conventional quantum many-body scars in a regime of weak disorder, remain unchanged. Around each of these states, the inverted quantum many-body scars are introduced by the increased disorder. Moreover, the strong disorder also gives rise to 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, reminiscent of conventional quantum many-body scarred states. Despite being the measure-zero states in the whole spectrum, these inverted quantum many-body scarred states significantly influence nonequilibrium dynamics in the large disorder regime. Random thermal states in a specific subspace show periodic revivals in the fidelity dynamics, while the typical charge-density-wave states exhibit persistent imbalance dynamics. We further examine the stability of the conventional and the inverted quantum many-body scars against the external random field. Our findings expand the variety of nonthermal systems and draw a connection between the weak violation of ergodicity and that of nonergodicity.
Isolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases.
We study the spin-1 XY model on a hypercubic lattice in d dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal long-range order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum many-body systems. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches-in other words, these eigenstates provide an archetypal example of so-called quantum many-body scars. This Letter opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena.
We propose physically reasonable systems capable of avoiding ergodicity at infinite time in the thermodynamic limit, even with generic perturbations and when coupled to a heat bath. In two dimensions, the rainbow loop soup has (stretched) exponentially numerous absolutely stable nonergodic states with diverging energy but vanishing energy density. In three dimensions the rainbow membrane soup has (stretched) exponentially numerous nonergodic states with diverging energy barriers, leading to infinite-time robust ergodicity breaking that even survives coupling to a nonzero temperature heat bath. We describe our results in the language of exact emergent symmetries and demonstrate how the systems avoid common instabilities. Our construction naturally connects to quantum dimer models, topologically ordered systems, the group word construction, and Hamiltonians whose low-energy eigenstates exhibit anomalous entanglement entropy.