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  • Open Access

Parent Hamiltonians for Stabilizer Quantum Many-Body Scars

Shane Dooley*

  • *Contact author: dooleysh@gmail.com
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Phys. Rev. Lett. 136, 240402 – Published 15 June, 2026

DOI: https://doi.org/10.1103/3vk5-483c

Abstract

Quantum many-body scars (QMBS) have attracted considerable interest due to their role in weak ergodicity breaking in many-body systems. We present a general construction that embeds stabilizer states as QMBS of local Hamiltonians. The method relies on a notion of factorizability of Pauli strings on a lattice, which is used to convert stabilizer elements into local, few-body operators that annihilate the stabilizer state. This enables the systematic construction of parent Hamiltonians with zero-energy stabilizer QMBS typically near the middle of the spectrum. The method reproduces several known results in a unified framework, including recent examples of volume-law entangled QMBS, such as the “rainbow” QMBS and the entangled antipodal Bell pair state. We also apply the framework to construct examples of stabilizer QMBS with a more complex entanglement structure, such as the cluster state, the toric code state, and a volume-law entangled state we dub the antipodal toric code state. Exact diagonalization confirms our results and reveal the stabilizer states as exact eigenstates of their parent Hamiltonian.

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Outline

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Phys. Rev. Lett. 136, 240402– Published 15 June, 2026
  • Received 20 January 2026
  • Accepted 27 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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