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arXiv:2603.03062 · Physical review. D/Physical review. D.

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

Sabhyata Gupta, Piotr Sierant, Luis Santos, Paolo Stornati

quant-phhep-latSubmitted Mar 3, 2026• Announced Mar 4, 2026• 0 citations
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Abstract

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.

Journal reference
Phys. Rev. D 113, 094509 , 2026
DOI
10.1103/hvdp-4m6
Comments
8 pages, 7 figures. Comments welcome!

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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.
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Quantum many-body scars are eigenstates in nonintegrable isolated quantum systems that defy typical thermalization paradigms, violating the eigenstate thermalization hypothesis and quantum ergodicity. We identify exact analytic scar solutions in a 2+1 dimensional lattice gauge theory in a quasi-1D limit as zero-magic resource stabilizer states. Our results also highlight the importance of magic resources for gauge theory thermalization, revealing a connection between computational complexity and quantum ergodicity.
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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
We construct a class of quantum many-body systems hosting an su(3)\mathfrak{su}(3)su(3)-invariant scar subspace, extending the conventional paradigm of quantum many-body scars beyond equally spaced spectra and single-directional tower structures. Our construction is based on local constraints that realize an algebraic closure within the scar subspace. As a result, the spectrum in the subspace is no longer equally spaced, but instead forms a multidirectional lattice structure parametrized by multiple independent quantum numbers. This leads to qualitatively new dynamical signatures: instead of single-frequency revivals, the system exhibits multifrequency oscillations governed by integer linear combinations of distinct energy scales. Importantly, the stability of the scar subspace does not rely on exact solvability of individual eigenstates. We show that algebraic closure preserves the invariant subspace even under perturbations that render the eigenstates analytically intractable, thereby realizing quantum many-body scars on an unsolvable reference state. Our results identify algebraic closure as a unifying mechanism underlying scar subspaces beyond the conventional su(2)\mathfrak{su}(2)su(2) paradigm, and open a route toward richer nonthermal dynamics in nonintegrable quantum systems.