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arXiv:2511.23395 · Physical Review Research

Hilbert space fragmentation in driven-dephasing Rydberg atom array

Tianyi Yan, Chun Hei Leung, Weibin Li

quant-phcond-mat.quant-gasphysics.atom-phSubmitted Nov 28, 2025• Announced Dec 1, 2025• 0 citations
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Abstract

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.

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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.
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.
Hilbert space fragmentation (HSF) is a mechanism for generating quantum many-body scar (QMBS), which provides a route to weakly break ergodicity. Many scarred systems possess an exponentially large number of zero-energy states due to the chiral symmetry induced bipartition of the Hilbert space. In this work, we study the QMBS phenomenology under the interplay between the chiral symmetry and pseudo HSF, where the Hilbert space is approximately fragmented into different blocks. We consider a model of tilted chain of interacting spinless fermions with periodically varying tunneling strength. At small tunneling strength, we analytically derive the resonance conditions under which the system is described by an effective model with chiral symmetry and pseudo HSF. We find that the interplay between the two gives rise to a highly localized zero-energy QMBS when the particle number is even. This zero-energy QMBS induces an unusual scarred dynamical phenomenon. Specifically, the fidelity from a simple initial state oscillates around a finite fixed value without decaying, instead of showing the typical decaying collapse and revival observed when the particle number is odd and in common scarred systems. We show that the signature of the unusual scarred dynamical behaviour can also be detected in the original driven system by measuring local observables. Our findings enrich the scar phenomenon and deepen the understanding of the relation between Hilbert space structure and QMBS.
We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems and find that it can stabilize highly entangled steady states. For concreteness, we consider the Temperley-Lieb model, which exhibits quantum HSF in an entangled basis, and investigate the Lindblad dynamics under two different couplings. First, we couple the system to a dephasing bath that reduces quantum fragmentation to a classical one with the resulting stationary state being separable. We observe that despite vanishing quantum correlations, classical correlations develop due to fluctuations of the remaining conserved quantities, which we show can be captured by a classical stochastic circuit evolution. Second, we use a coupling that preserves the quantum fragmentation structure. We derive a general expression for the steady state, which has a strong coherent memory of the initial state due to the extensive number of noncommuting conserved quantities. We then show that it is highly entangled as quantified by logarithmic negativity.
Hilbert space fragmentation (HSF) is a mechanism for generating quantum many-body scar (QMBS), which provides a route to weakly break ergodicity. The zero-energy QMBSs widely exist across various systems due to the intertwining of chiral symmetry and spatial inversion symmetry. In this work, we study the phenomenology of the zero-energy QMBS under the interplay between the chiral symmetry and pseudo HSF, where the Hilbert space is approximately fragmented into different blocks. We consider a model of tilted chain of interacting spinless fermions with periodically varying tunneling strength. At small tunneling strength and under resonance condition, the system is described by an effective model with chiral symmetry and pseudo HSF. We find that the interplay between the two gives rise to a highly localized zero-energy QMBS when the particle number is even. We identify a simple product state to signalize the zero-energy QMBS, which gives rise to unusual scarred dynamics. The fidelity oscillates around a fixed value without decaying instead of showing the usual collapse and revival in common scarred systems. We show that the signature of the zero-energy QMBS can also be captured by the original Hamiltonian. Our results uncover a new scar phenomenon and provide an example that does not need the intertwining of chiral and spatial symmetries to support zero-energy QMBS.
While isolated quantum systems generally thermalize after long-time evolution, there are several exceptions defying thermalization. A notable mechanism of this nonergodicity is the Hilbert space fragmentation (HSF), where the Hamiltonian matrix splits into an exponentially large number of sectors due to the presence of nontrivial conserved quantities. Using ultracold gases, here, we experimentally investigate the one-dimensional Bose-Hubbard system with neither disorder nor tilt potential, which has been predicted to exhibit HSF caused by a strong interatomic interaction. Specifically, we analyze far-from-equilibrium dynamics starting from a charge density wave of doublons (atoms in doubly occupied sites) in a singlon- and doublon-resolved manner to reveal a slowing down of the relaxation in a strongly interacting regime. We find that the numbers of singlons and doublons are conserved during the dynamics, indicating HSF as a mechanism of the observed slow relaxation. Our results provide an experimental confirmation of the conserved quantities responsible for HSF.
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-SU(2)\text{SU}(2)SU(2)'' algebra discovered in the context of many-body scarring.