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arXiv:2502.02959 · Science Advances

Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains

Kantaro Honda, Yosuke Takasu, Shimpei Goto, Hironori Kazuta, Masaya Kunimi, Ippei Danshita, Yoshiro Takahashi

Published Jun 6, 2025• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/sciadv.adv3255

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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.
We study Hilbert-space fragmentation and thermalization in a one-dimensional dipole-conserving Bose-Hubbard chain. By analyzing the structure of the Hamiltonian matrix in the Fock basis, we show that the system exhibits weak Hilbert-space fragmentation. We further construct an exponentially large family of frozen product states and derive analytical upper and lower bounds on their number. Using exact diagonalization, we examine the consequences of weak fragmentation for eigenstate half-chain entanglement, density relaxation dynamics, and level statistics. All these quantities reveal a transition from a weak eigenstate thermalization regime to a nonergodic regime with increasing on-site interaction strength. These results show that weak Hilbert-space fragmentation \textit{does not} preclude quantum chaos or thermalization, and provides a minimal platform for studying the interplay of dipole conservation, weak fragmentation, and ergodicity breaking.
The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm due to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which thermalisation can be strongly suppressed. Here, we experimentally observe Hilbert space fragmentation (HSF) in a two-dimensional tilted Bose-Hubbard model. Using quantum gas microscopy, we engineer a wide variety of initial states and find a rich set of manifestations of HSF involving bulk states, interfaces and defects, i.e., d = 2, 1 and 0 dimensional objects. Specifically, uniform initial states with equal particle number and energy differ strikingly in their relaxation dynamics. Inserting controlled defects on top of a global, non-thermalising chequerboard state, we observe highly anisotropic, sub-dimensional dynamics, an immediate signature of their fractonic nature. An interface between localized and thermalising states in turn displays dynamics depending on its orientation. Our results mark the first observation of HSF beyond one dimension, as well as the concomitant direct observation of fractons, and pave the way for in-depth studies of microscopic transport phenomena in constrained systems
Intriguingly, quantum many-body systems may defy thermalization even without disorder. One example is so-called fragmented models, where the many-body Hilbert space fragments into dynamically disconnected subspaces that are not determined by the global symmetries of the model. In this Letter we demonstrate that the tilted one-dimensional Fermi-Hubbard model naturally realizes distinct effective Hamiltonians that are expected to support nonergodic behavior due to fragmentation, even at resonances between the tilt energy and the Hubbard on site interaction. We find that the effective description captures the observed dynamics in experimentally accessible parameter ranges of moderate tilt values. Specifically, we observe a pronounced dependence of the relaxation dynamics on the initial doublon fraction, which directly reveals the microscopic processes of the fragmented model. Our results pave the way for future studies of nonergodic behavior in higher dimensions.
Quantum many-body systems may defy thermalization even without disorder. Intriguingly, non-ergodicity may be caused by a fragmentation of the many-body Hilbert-space into dynamically disconnected subspaces. The tilted one-dimensional Fermi-Hubbard model was proposed as a platform to realize fragmented models perturbatively in the limit of large tilt. Here, we demonstrate the validity of this effective description for the transient dynamics using ultracold fermions. The effective analytic model allows for a detailed understanding of the emergent microscopic processes, which in our case exhibit a pronounced doublon-number dependence. We study this experimentally by tuning the doublon fraction in the initial state.
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 propose the strongly tilted Bose-Hubbard model as a natural platform to explore Hilbert-space fragmentation (HSF) and fracton dynamics in two dimensions in a setup and regime readily accessible in optical lattice experiments. Using a perturbative ansatz, we find HSF when the model is tuned to the resonant limit of on-site interaction and tilted potential. First, we investigate the quench dynamics of this system and observe numerically that the relaxation dynamics strongly depends on the chosen initial state-one of the key signatures of HSF. Second, we identify fractonic excitations with restricted mobility leading to anomalous transport properties. Specifically, we find excitations that show one-dimensional diffusion (z=1/2) as well as excitations that show subdiffusive behavior in two dimensions (z=3/4). Using a cellular automaton, we analyze their dynamics and compare it to an effective hydrodynamic description.