Generalized Shiraishi--Mori construction is exhaustive for ferromagnetic quantum many-body scars
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Quantum Physics arXiv:2601.11806 (quant-ph) [Submitted on 16 Jan 2026] Title:Generalized Shiraishi--Mori construction is exhaustive for ferromagnetic quantum many-body scars Authors:Keita Omiya View a PDF of the paper titled Generalized Shiraishi--Mori construction is exhaustive for ferromagnetic quantum many-body scars, by Keita Omiya View PDF HTML (experimental) Abstract:Quantum many-body scars (QMBS) constitute a subtle violation of ergodicity through a set of non-thermal eigenstates, referred to as scar states, which are embedded in an otherwise thermal spectrum. In a broad class of known examples, these scar states admit a simple interpretation: they are magnon excitations of fixed momentum on top of a ferromagnetic background. In this paper we prove that any Hamiltonian hosting such ``ferromagnetic scar states'' necessarily admits a structural decomposition into a Zeeman term and an ``annihilator'' that annihilates the entire scar manifold. Moreover, we show that this annihilator must itself decompose into a sum of terms built from local projectors that locally annihilate the scar states. This architecture is closely related to the Shiraishi--Mori construction, and our main theorem establishes that an appropriate generalization of that construction is in fact essentially exhaustive for this class of scar states. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph) Cite as: arXiv:2601.11806 [quant-ph] (or arXiv:2601.11806v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.11806 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Keita Omiya [view email] [v1] Fri, 16 Jan 2026 22:15:50 UTC (65 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalized Shiraishi--Mori construction is exhaustive for ferromagnetic quantum many-body scars, by Keita OmiyaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.str-el math math-ph math.MP 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?)