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.
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.
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 introduce a disorder-free model of S=1/2 S = 1 / 2 spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.
We investigate a mechanism for nonergodic behavior arising from destructive interference in Fock space, leading to (FSCs)—exact zero-energy eigenstates localized on O ( 1 ) to O ( L p ) configurations within an exponentially large connected Krylov sector. Unlike many-body localization or Hilbert space fragmentation, FSCs emerge from graph-theoretic interference cancellations in disorder-free kinetically constrained systems with chiral symmetry. We develop systematic algorithms that enable explicit construction of these cages in four representative models, revealing this as a universal mechanism for kinetically constrained systems with chiral symmetry. Dynamically, FSCs produce persistent plateaus in the Loschmidt echo and magnetization: return probabilities scale as L − 2 for O ( L ) cages and remain O ( 1 ) for ultralocal ones, while the magnetization saturates to O ( 1 ) instead of decaying to zero. This may provide new routes for engineering long-lived nonthermal states in quantum simulation platforms.
We find that rank deficiency of the local Hamiltonian in a classically fragmented model is the key mechanism leading to quantum Hilbert space fragmentation. The rank deficiency produces local null directions that can generate entangled frozen states (EFS): entangled states embedded in mobile classical Krylov sectors that do not evolve under Hamiltonian dynamics. When the entangled frozen subspace is non-empty, the mobile classical sector splits into a mobile quantum Krylov subspace and an entangled frozen subspace, and the model exhibits quantum fragmentation. We establish this mechanism in four models of increasing symmetry structure: an asymmetric qubit projector with no symmetry, the Z2-symmetric GHZ projector, a Z3-symmetric cyclic qutrit projector, and the Temperley-Lieb model. For the asymmetric and GHZ projector models, we obtain closed-form expressions for irreducible Krylov dimensions, degeneracies, and sector multiplicities. The all-mobile-sector EFS in these two models exhibits a sub-volume-law bipartite entanglement entropy scaling as S∼L. Further, we introduce the notion of weak and strong quantum fragmentation, the quantum counterpart of the weak-strong distinction in classical fragmentation. After removing the EFS, the mobile quantum Krylov subspace decomposes into irreducible blocks. In the weak case, the number of irreducible blocks remains O(1), each is individually ergodic with Gaussian Orthogonal Ensemble (GOE) level statistics, and the unresolved spectrum follows an mGOE distribution. In the strong case, the number of irreducible blocks grows with system size, and the gap-ratio distribution approaches Poisson as L→∞.
We investigate a one-dimensional correlated-hopping model of spinless fermions with an East constraint. We first analytically unravel the complete fragmentation structure of this model by labeling each fragment by a unique root configuration and utilizing the transfer matrix method. We show that the growth of the size of each fragment of the model follows the widely studied Dyck sequence and is therefore analytically tractable with the help of Catalan triangles. While the eigenstate thermalization hypothesis (ETH) does not hold within the full Hilbert space which exhibits Poisson statistics of the energy level spacing, an examination of various quantities restricted to the largest fragments shows that a weaker version of the subspace-restricted thermalization holds. This weaker violation of the ETH within the largest fragments is supported by the presence of subspace-restricted quantum many-body scars due to quantum fragmentation. Our analysis further reveals that the filling fraction at which the model has the largest fragment shifts with increasing system sizes from half-filling due to the distinct fragmentation structure. Next, we show that the inclusion of a nearest-neighbor density-density interaction with strength V induces a spectral transition within the largest fragment from a weakly ETH-violating phase containing scars to a statistical bubble localized phase as V increases. In particular, the $V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit produces an integrable model. We find that the addition of finite-V stabilizes the ground state near half-filling while keeping intact the fragmentation structure of the East model. However, this behavior abruptly changes exactly at $V=\ensuremath{\infty}$ due to the emergence of a distinct fragmentation structure; we analytically explore this in a comprehensive manner. The infinite-V model has many interesting properties, among which the appearance of the ground state and the largest fragment at two different filling fractions is specially noteworthy. Finally, we propose an experimental setup to realize the infinite-V model as a particular limit of a special kind of $t\text{\ensuremath{-}}V$ model with an on-site potential.
Quantum thermalization occurs in a broad class of systems from elementary particles to complex materials. Out-of-equilibrium quantum systems have long been understood to either thermalize or retain memory of their initial states, but not both. Here, we achieve the first coexistence of thermalization and memory in a quantum system, where we use both Rydberg blockade and facilitation in an atom array to engineer a fragmentation of the Hilbert space into exponentially many disjointed subspaces. We find that the kinetically constrained system yields quantum many-body scars arising from the Z 2 k class of initial states, which generalizes beyond the Z 2 scars previously reported in other quantum systems. When bringing multiple long-range interactions into resonance, we observe quantum thermalization restricted to Hilbert space fragments, where the thermalized system retains characteristics of the initial configuration. Intriguingly, states belonging to different subspaces do not thermalize with each other even when they have the same energy. Our work sheds light on a subtle aspect of quantum thermalization while experimentally resolving the long-standing tension between thermalization and memory. These results may be applied to control entanglement dynamics in quantum processors and quantum sensors.