Parent Hamiltonians for stabilizer quantum many-body scars

Quantum Physics arXiv:2601.10805 (quant-ph) [Submitted on 15 Jan 2026] Title:Parent Hamiltonians for stabilizer quantum many-body scars Authors:Shane Dooley View a PDF of the paper titled Parent Hamiltonians for stabilizer quantum many-body scars, by Shane Dooley View PDF HTML (experimental) 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 (ATC) state. Exact diagonalization confirms our results and reveal the stabilizer states as exact eigenstates of their parent Hamiltonian. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Report number: DIAS-STP-26-01 Cite as: arXiv:2601.10805 [quant-ph] (or arXiv:2601.10805v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.10805 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shane Dooley [view email] [v1] Thu, 15 Jan 2026 19:15:57 UTC (3,743 KB) Full-text links: Access Paper: View a PDF of the paper titled Parent Hamiltonians for stabilizer quantum many-body scars, by Shane DooleyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)