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

Sabhyata Gupta1,*, Piotr Sierant2,†, Luis Santos1,‡, and Paolo Stornati2,§

  • *Contact author: sabhyata.gupta@itp.uni-hannover.de
  • †Contact author: piotr.sierant@bsc.es
  • ‡Contact author: santos@itp.uni-hannover.de
  • §Contact author: paolo.stornati@bsc.es
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Phys. Rev. D 113, 094509 – Published 28 May, 2026

DOI: https://doi.org/10.1103/hvdp-4m6f

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.

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Phys. Rev. D 113, 094509– Published 28 May, 2026
  • Received 11 March 2026
  • Accepted 14 May 2026
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