In this Letter, we report a parameter-dependent Hilbert space fragmentation in a one-dimensional Rydberg atom array under anti-blockade conditions. We identify distinct non-equilibrium dynamical phases and show that their quasi-periodic behavior arises from the interplay of multi-path interference and multi-photon cascaded excitations, reflecting fundamental differences in state connectivity and effective dimensionality. By constructing a complete phase diagram, we reveal the transition from thermalization to fragmentation, and further demonstrate a secondary fragmentation process enabled by local constraints. Our results highlight the potential of anti-blockade mechanisms for programmable non-thermal dynamics in many-body systems.
In this Letter, we report a parameter-dependent Hilbert space fragmentation in a one-dimensional Rydberg atom array under anti-blockade conditions. We identify distinct non-equilibrium dynamical phases and show that their quasi-periodic behavior arises from the interplay of multi-path interference and multi-photon cascaded excitations, reflecting fundamental differences in state connectivity and effective dimensionality. By constructing a complete phase diagram, we reveal the transition from thermalization to fragmentation, and further demonstrate a secondary fragmentation process enabled by local constraints. Our results highlight the potential of anti-blockade mechanisms for programmable non-thermal dynamics in many-body systems.
In a strongly interacting Rydberg atom array, the dynamics are often constrained to the decoupled Hilbert subspaces, representing an intriguing paradigm for nonergodicity. By considering a variable detuning of the global Rydberg coupling, we show that, not only is the existence of these Hilbert subspaces dependent on the interplay of detuning and interaction, but they are also strongly fragmented, with the fragment dimensions exhibiting various scaling behaviors with increasing system size. The resulting constrained dynamics of the system are thus governed by the dimension and connectivity of these fragments. We then adopt an auxiliary fermion description to reveal the underlying emergent kinetic constraints for the subspace fragmentation and fragment-confined dynamics. Our results provide a systematic understanding of Hilbert-space fragmentation in Rydberg arrays, and shed light on engineering nonergodic many-body dynamics beyond the PXP model.
We investigate the onset and mechanism of Hilbert space fragmentation (HSF) in a chain of strongly interacting Rydberg atoms subject to local dephasing. It is found that the emergence of multiple long-lived metastable states is fundamentally tied to HSF of the driven-dephasing Rydberg atom system. We demonstrate that the manifesting HSF is captured by a dephasing PXP model that supports multiple degenerate zero modes. These modes form disconnected, block-diagonal subspaces of maximally mixed states, which consist of many-body spin states sharing the same symmetry. A key result is the identification of the underlying symmetry in the HSF, where conserved quantities in each subspace are defined by the consecutive double excitation addressing operator. Moreover, we show explicitly that the number of the fragmented Hilbert space grows exponentially with the chain length, following a modified Fibonacci sequence. Our work provides insights into many-body dynamics under dynamical constraints and opens avenues for controlling and manipulating HSF in Rydberg atom systems.
We demonstrate emergent Hilbert-space fragmentation in a composite chain of PXP and dual-PXP subchains separated by junctions with simultaneous blockade and anti-blockade projection constraints. The Hilbert space shatters into disjoint Krylov fragments growing exponentially with junction number. Freezing does not require a unique allowed junction state: multiple configurations remain locally allowed, but the dual constraints remove dynamical links between them. Each fragment is labeled by frozen junction configurations and contains compatible basis states. This fragmentation produces dynamical caging of quantum information between neighboring junctions and novel states with partially thermal and athermal regions. Softening the junction by admitting other local states with variable nonzero diagonal amplitudes destroys the direct-sum block structure and fragmentation. Nevertheless, information remains dynamically insulated and inhomogeneous thermal properties persist up to an onset time scaling with the diagonal energy penalty of the previously restricted junction states, followed by longer prethermal behavior. Energy-level statistics in each symmetry-resolved sector evolve from Poissonian in the hard-junction limit toward Wigner-Dyson behavior upon softening, with finite-size non-monotonicity. This signals the breakdown of the tensor-sum structure yielding pairwise sums of chaotic subchain spectra, restoring chaotic thermalization. In the hard-junction case, we find a chirally protected zero-energy mode with density peaks at physical edges and near the junction, pinned to zero under chirality-preserving disorder. The tensor-product eigenfunction structure also enhances the number of nonzero-energy scar states. Finally, we discuss routes to these junction architectures in programmable Rydberg atom platforms using optical tweezers, local addressing, and facilitation techniques.
Kinetic constraints in quantum many-body systems strongly restrict the accessible Hilbert space, giving rise to highly nontrivial dynamical behavior. In recent years, such systems have attracted growing interest as they provide insight into mechanisms of thermalization and into regimes where thermalization fails. In this work, we study a family of rule-based kinetically constrained models, including the celebrated Quantum Game of Life, from the perspective of quantum complexity, with a focus on entanglement, nonstabilizerness, and quantum chaos. Using spectral diagnostics such as level statistics and spectral form factors, we show that these models exhibit robust chaotic behavior while simultaneously supporting both strong and weak Hilbert-space fragmentation and quantum many-body scar states. Our results reveal that the nature of Hilbert-space fragmentation can be tuned qualitatively from strong to weak fragmentation and ultimately to its absence, within a single family of models through simple variations of the underlying kinetic rules. To further elucidate the structure of these fragmented subspaces, we characterize them through their ability to generate quantum resources. In particular, we show that resource-generation capacity does not necessarily correlate with the dimensionality of a fragmented sector, and that entanglement structure and the ability to generate nonstabilizerness provide effective diagnostics for distinguishing dynamically disconnected sectors, including those supporting nonthermal scarred dynamics. Our work thus places kinetically constrained models within a broader and more general framework, not limited to Rydberg blockade based constraints only, and demonstrates that simple variations in underlying rules can lead to qualitatively distinct static and dynamical regimes including chaotic, fragmented, and scarred phases.
The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.
Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.