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arXiv:2506.10806 · Physical review. B./Physical review. B

Constructing quantum many-body scars from weak Hilbert space fragmentation

Fan Yang, Matteo Magoni, Hannes Pichler

Published Apr 10, 2026• 1 citation
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Abstract

Quantum many-body scars (QMBS) are exotic many-body states that exhibit anomalous nonthermal behavior in an otherwise ergodic system. In this work, we demonstrate a simple, scalable, and intuitive construction of QMBS in a kinetically constrained quantum model exhibiting weak Hilbert space fragmentation. We show that exact QMBS can be constructed by injecting a quasiparticle that partially activates the frozen regions in the lattice. Meanwhile, the inelastic collision between multiple quasiparticles allows for the construction of approximate scars, whose damping is governed by an emergent two-body loss. Our findings establish direct connections between quantum many-body scarring and Hilbert space fragmentation, paving the way for systematically constructing exact and approximate QMBS with nontrivial spatial connectivity. The proposed model can be readily implemented in neutral-atom quantum simulators aided by strong Rydberg interactions.

DOI
10.1103/cpt2-kqdy

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Quantum many-body scars (QMBS) are exotic many-body states that exhibit anomalous nonthermal behavior in an otherwise ergodic system. In this work, we demonstrate a simple, scalable, and intuitive construction of QMBS in a kinetically constrained quantum model exhibiting weak Hilbert space fragmentation. We show that exact QMBS can be constructed by injecting a quasiparticle that partially activates the frozen regions in the lattice. Meanwhile, the inelastic collision between multiple quasiparticles allows for the construction of approximate scars, whose damping is governed by an emergent two-body loss. Our findings establish direct connections between quantum many-body scarring and Hilbert space fragmentation, paving the way for systematically constructing exact and approximate QMBS with nontrivial spatial connectivity. The proposed model can be readily implemented in neutral-atom quantum simulators aided by strong Rydberg interactions.
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.
Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well defined in generic many-body systems owing to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual nonequilibrium phenomena including many-body revivals and nonthermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles.
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.
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.
Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium. An example of such nonthermalizing behavior is the phenomenon of quantum many-body scars, which has been experimentally observed in Rydberg-atom quantum simulators. Here, the authors show that many-body scars can generally be viewed as forming approximate subspaces of ``broken'' Lie algebra representations. Furthermore, they use an iterative process to identify perturbations which ``correct'' the broken Lie algebra, resulting in improved quantum revivals from special initial states. The description of embedded Lie algebra representations unifies several theoretical models, which feature exact many-body scars, with experimentally realized models, such as the constrained Rydberg-atom system, where scars only form an approximate Lie algebra representation.
The concept of quantum many-body scars has recently been put forward as a route to describe weak ergodicity breaking and violation of the eigenstate thermalization hypothesis. We propose a simple setup to generate quantum many-body scars in a doubly modulated Bose-Hubbard system which can be readily implemented in cold atomic gases. The dynamics are shown to be governed by kinetic constraints which appear via density-assisted tunneling in a high-frequency expansion. We find the optimal driving parameters for the kinetically constrained hopping which leads to small isolated subspaces of scared eigenstates. The experimental signatures and the transition to fully thermalizing behavior as a function of driving frequency are analyzed.