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

Quantum scars from zero modes in an Abelian lattice gauge theory

Debasish Banerjee, Arnab Sen

Published Dec 15, 2020• 4 citations
OpenAlex

Abstract

We consider the spectrum of a $U(1)$ quantum link model where gauge fields are realized as $S=1/2$ quantum spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian $H={\cal O}_{\rm kin}+\lambda {\cal O}_{\rm pot}$, where ${\cal O}_{\rm pot}$ (${\cal O}_{\rm kin}$) is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at $\lambda=0$ whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero $\lambda$ but some special linear combinations that simultaneously diagonalize ${\cal O}_{\rm kin}$ and ${\cal O}_{\rm pot}$ survive as quantum many-body scars, suggesting an order-by-disorder mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on ladders with up to $56$ spins, which may be tested using available proposals of quantum simulators.

Related papers

Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory on Ladders

Debasish Banerjee, Arnab Sen

We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.

arXiv:2012.08540•Physical Review Letters•Jun 4, 2021•107 citations

Sublattice scars and beyond in two-dimensional U(1) quantum link lattice gauge theories

Indrajit Sau, Paolo Stornati, Debasish Banerjee +1 more

In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is H=Okin+λOpot , where λ is a real-valued coupling, and Okin ( Opot ) are summed local off-diagonal (diagonal) operators in the electric flux basis acting on the elementary plaquette □ . The spectrum of the model in its spin- 12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩ , which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin . We demonstrate a “triangle relation” connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=0 eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of Okin become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another U(1) quantum link model with a staggered short-ranged diagonal term. Published by the American Physical Society 2024

arXiv:2311.06773•Physical review. D/Physical review. D.•Feb 27, 2024•16 citations

Exact stabilizer scars in two-dimensional $U(1)$ lattice gauge theory

Sabhyata Gupta, Piotr Sierant, Luis Santos +1 more

The complexity of highly excited eigenstates is a central theme in nonequilibrium many-body physics, underpining questions of thermalization, classical simulability, and quantum information structure. In this work, considering the paradigmatic Rokhsar-Kivelson model, we connect quantum many-body scarring in Abelian lattice gauge theories to an emergent stabilizer structure. We identify a distinct class of scarred eigenstates, termed sublattice scars, originating from gauge-invariant zero modes that form exact stabilizer states. Remarkably, although the underlying Hamiltonian is not a stabilizer Hamiltonian, its eigenspectrum intrinsically hosts exact stabilizer eigenstates. These sublattice scars exhibit vanishing stabilizer Rényi entropy together with finite, highly structured entanglement, enabling efficient classical simulation. Exploiting their stabilizer structure, we construct explicit Clifford circuits that prepare these states in a two-dimensional lattice gauge model. Our results demonstrate that the scarred subspace of the Rokhsar-Kivelson spectrum forms an intrinsic stabilizer manifold, revealing a direct connection between stabilizer quantum information, lattice gauge constraints, and quantum many-body scarring.

quant-pharXiv:2603.03062•Physical review. D/Physical review. D.•Mar 4, 2026•0 citations

Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models

S. N. Biswas, Debasish Banerjee, Arnab Sen

We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in U(1) U ( 1 ) quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian H=\mathcal{O}_{\mathrm{kin}} + \lambda \mathcal{O}_{\mathrm{pot}} H = 𝒪 k i n + λ 𝒪 p o t where \mathcal{O}_{\mathrm{pot}} 𝒪 p o t ( \mathcal{O}_{\mathrm{kin}} 𝒪 k i n ) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at \lambda=0 λ = 0 that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for |\lambda| \lesssim \mathcal{O}(1) | λ | ≲ 𝒪 ( 1 ) both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite \lambda λ show a rich variety with those that are composed solely from the zero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , those that contain an admixture of both the zero and the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , and finally those composed solely from the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n

arXiv:2202.03451•SciPost Physics•May 6, 2022•45 citations

Robust quantum many-body scars in lattice gauge theories

Jad C. Halimeh, Luca Barbiero, Philipp Hauke +2 more

Quantum many-body scarring is a paradigm of weak ergodicity breaking arising due to the presence of special nonthermal many-body eigenstates that possess low entanglement entropy, are equally spaced in energy, and concentrate in certain parts of the Hilbert space. Though scars have been shown to be intimately connected to gauge theories, their stability in such experimentally relevant models is still an open question, and it is generally considered that they exist only under fine-tuned conditions. In this work, we show through Krylov-based time-evolution methods how quantum many-body scars can be made robust in the presence of experimental errors through utilizing terms linear in the gauge-symmetry generator or a simplified pseudogenerator in U(1) and Z2 lattice gauge theories. Our findings are explained by the concept of quantum Zeno dynamics. Our experimentally feasible methods can be readily implemented in existing large-scale ultracold-atom quantum simulators and setups of Rydberg atoms with optical tweezers.

arXiv:2203.08828•Quantum•May 15, 2023•41 citations

Weak ergodicity breaking in the Schwinger model

Jean-Yves Desaules, Debasish Banerjee, Ana Hudomal +3 more

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-$\frac{1}{2}$ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for $S>\frac{1}{2}$ since such theories converge to the lattice Schwinger model in the large-$S$ limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-$S\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)$ quantum link models (QLMs) with staggered fermions. We find that QMBS persist at $S>\frac{1}{2}$, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial product states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-$S$ QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.

arXiv:2203.08830•Physical review. B./Physical review. B•May 5, 2023•71 citations
We consider the spectrum of a U(1)U(1)U(1) quantum link model where gauge fields are realized as S=1/2S=1/2S=1/2 quantum spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian H=Okin+λOpotH={\cal O}_{\rm kin}+\lambda {\cal O}_{\rm pot}H=Okin​+λOpot​, where Opot{\cal O}_{\rm pot}Opot​ (Okin{\cal O}_{\rm kin}Okin​) is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at λ=0\lambda=0λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero λ\lambdaλ but some special linear combinations that simultaneously diagonalize Okin{\cal O}_{\rm kin}Okin​ and Opot{\cal O}_{\rm pot}Opot​ survive as quantum many-body scars, suggesting an order-by-disorder mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on ladders with up to 565656 spins, which may be tested using available proposals of quantum simulators.
We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.
In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is H=Okin+λOpot , where λ is a real-valued coupling, and Okin ( Opot ) are summed local off-diagonal (diagonal) operators in the electric flux basis acting on the elementary plaquette □ . The spectrum of the model in its spin- 12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩ , which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin . We demonstrate a “triangle relation” connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=0 eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of Okin become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another U(1) quantum link model with a staggered short-ranged diagonal term. Published by the American Physical Society 2024
Exact stabilizer scars in two-dimensional U(1)U(1)U(1) lattice gauge theory
The complexity of highly excited eigenstates is a central theme in nonequilibrium many-body physics, underpining questions of thermalization, classical simulability, and quantum information structure. In this work, considering the paradigmatic Rokhsar-Kivelson model, we connect quantum many-body scarring in Abelian lattice gauge theories to an emergent stabilizer structure. We identify a distinct class of scarred eigenstates, termed sublattice scars, originating from gauge-invariant zero modes that form exact stabilizer states. Remarkably, although the underlying Hamiltonian is not a stabilizer Hamiltonian, its eigenspectrum intrinsically hosts exact stabilizer eigenstates. These sublattice scars exhibit vanishing stabilizer Rényi entropy together with finite, highly structured entanglement, enabling efficient classical simulation. Exploiting their stabilizer structure, we construct explicit Clifford circuits that prepare these states in a two-dimensional lattice gauge model. Our results demonstrate that the scarred subspace of the Rokhsar-Kivelson spectrum forms an intrinsic stabilizer manifold, revealing a direct connection between stabilizer quantum information, lattice gauge constraints, and quantum many-body scarring.
Scars from protected zero modes and beyond in U(1)U(1)U(1) quantum link and quantum dimer models
We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in U(1) U ( 1 ) quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian H=\mathcal{O}_{\mathrm{kin}} + \lambda \mathcal{O}_{\mathrm{pot}} H = 𝒪 k i n + λ 𝒪 p o t where \mathcal{O}_{\mathrm{pot}} 𝒪 p o t ( \mathcal{O}_{\mathrm{kin}} 𝒪 k i n ) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at \lambda=0 λ = 0 that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for |\lambda| \lesssim \mathcal{O}(1) | λ | ≲ 𝒪 ( 1 ) both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite \lambda λ show a rich variety with those that are composed solely from the zero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , those that contain an admixture of both the zero and the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , and finally those composed solely from the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n
Quantum many-body scarring is a paradigm of weak ergodicity breaking arising due to the presence of special nonthermal many-body eigenstates that possess low entanglement entropy, are equally spaced in energy, and concentrate in certain parts of the Hilbert space. Though scars have been shown to be intimately connected to gauge theories, their stability in such experimentally relevant models is still an open question, and it is generally considered that they exist only under fine-tuned conditions. In this work, we show through Krylov-based time-evolution methods how quantum many-body scars can be made robust in the presence of experimental errors through utilizing terms linear in the gauge-symmetry generator or a simplified pseudogenerator in U(1) and Z2 lattice gauge theories. Our findings are explained by the concept of quantum Zeno dynamics. Our experimentally feasible methods can be readily implemented in existing large-scale ultracold-atom quantum simulators and setups of Rydberg atoms with optical tweezers.
As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-12\frac{1}{2}21​ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for S>12S>\frac{1}{2}S>21​ since such theories converge to the lattice Schwinger model in the large-SSS limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-SU(1)S\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)SU(1) quantum link models (QLMs) with staggered fermions. We find that QMBS persist at S>12S>\frac{1}{2}S>21​, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial product states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-SSS QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.