Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fragmentation, zero modes, and collective bound states in constrained models

Eulàlia Nicolau Jiménez, Marko Ljubotina, Maksym Serbyn

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.

Related papers

Fragmentation, Zero Modes, and Collective Bound States in Constrained Models

Eulàlia Nicolau, Marko Ljubotina, Maksym Serbyn

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as —stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U ( 1 ) particle-conservation symmetry. We use the U ( 1 ) East, which lacks inversion symmetry, and the inversion-symmetric U ( 1 ) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of , a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U ( 1 ) North-East, and in the pair-flip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.

arXiv:2504.17627•PRX Quantum•Jan 30, 2026•6 citations

Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models

Pietro Brighi, Marko Ljubotina, Maksym Serbyn

Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored dynamical behavior and invite their further theoretical and experimental studies.

arXiv:2210.15607•SciPost Physics•Sep 13, 2023•48 citations

Localized Fock space cages in kinetically constrained models

Cheryne Jonay, Frank Pollmann

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.

arXiv:2504.20987•Physical review. B./Physical review. B•Apr 9, 2026•6 citations

Freezing transition in the particle-conserving East model

Cheng Wang, Zhi-Cheng Yang

Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle-number-conserving systems in which particle hoppings are subjected to an East-like constraint, akin to facilitated spin models in classical glasses. While such a kinetic constraint leads to HSF, we find that the degree of fragmentation exhibits a sharp transition as the average particle density is varied. Below a critical density, the system transitions from being weakly fragmented where most of the initial states thermalize diffusively to strongly fragmented where the dynamics are frozen and the system fails to thermalize. Remarkably, the East model allows for both efficient numerical simulations and analytic solutions of various diagnostics of the phase transition, from which we obtain a set of exact critical exponents. We find that the freezing transition in particle-conserving East models belongs to the same universality class as dipole-conserving fracton systems. Our results provide a tractable minimal model for filling-induced freezing transitions associated with HSF, which can be readily tested on state-of-the-art quantum platforms.

arXiv:2307.01993•Physical review. B./Physical review. B•Oct 31, 2023•10 citations

Emergent Kinetic Constraints and Subspace Fragmentation in Rydberg Arrays

Wen-Jie Geng, Zhenming Zhang, Wei Yi

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.

cond-mat.quant-gasCross-listedarXiv:2605.01366•May 5, 2026•0 citations

Zero-energy Quantum Many-Body Scar under Emergent Chiral Symmetry and Pseudo Hilbert Space Fragmentation

Zhang, Li, Yongguan Ke, Chaohong Lee

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.

arXiv:2410.22778•Oct 30, 2024•0 citations
Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.
Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as —stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U ( 1 ) particle-conservation symmetry. We use the U ( 1 ) East, which lacks inversion symmetry, and the inversion-symmetric U ( 1 ) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of , a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U ( 1 ) North-East, and in the pair-flip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored dynamical behavior and invite their further theoretical and experimental studies.
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.
Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle-number-conserving systems in which particle hoppings are subjected to an East-like constraint, akin to facilitated spin models in classical glasses. While such a kinetic constraint leads to HSF, we find that the degree of fragmentation exhibits a sharp transition as the average particle density is varied. Below a critical density, the system transitions from being weakly fragmented where most of the initial states thermalize diffusively to strongly fragmented where the dynamics are frozen and the system fails to thermalize. Remarkably, the East model allows for both efficient numerical simulations and analytic solutions of various diagnostics of the phase transition, from which we obtain a set of exact critical exponents. We find that the freezing transition in particle-conserving East models belongs to the same universality class as dipole-conserving fracton systems. Our results provide a tractable minimal model for filling-induced freezing transitions associated with HSF, which can be readily tested on state-of-the-art quantum platforms.
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. 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.