Unified theory of local integrals of motion

[2512.09595] Unified theory of local integrals of motion Skip to main content Search Submit Donate Log in Condensed Matter > Disordered Systems and Neural Networks arXiv:2512.09595 (cond-mat) [Submitted on 10 Dec 2025 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Unified theory of local integrals of motion Authors: Ben Craps , Oleg Evnin , Dmitry Kovrizhin , Gabriele Pascuzzi View PDF HTML (experimental) Abstract: Conservation laws are of paramount importance in our understanding of classical and quantum dynamics. Here, we present a general framework for constructing exact quantum integrals of motion with the desired locality and quantum numbers, which will be illustrated for the case of many-body-localization (MBL). The latter has been understood theoretically in terms of the existence of an extensive number of local integrals of motion (LIOMs). Using our approach, we show that one can express the task of finding LIOMs as an optimization problem. For some specifications, this problem surprisingly connects to the question of finding classical ground states of spin-glass models. Our work unifies previous results obtained in the MBL context and reveals intriguing connections between many-body localization, spin-glass physics, and constrained optimization problems. Comments: v2: accepted for publication Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2512.09595 [cond-mat.dis-nn] (or arXiv:2512.09595v2 [cond-mat.dis-nn] for this version) https://doi.org/10.48550/arXiv.2512.09595 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 114 (2026) L140201 Related DOI : https://doi.org/10.1103/xmqc-99hq Focus to learn more DOI(s) linking to related resources Submission history From: Oleg Evnin [ view email ] [v1] Wed, 10 Dec 2025 12:44:12 UTC (33 KB) [v2] Tue, 25 Aug 2026 03:54:28 UTC (35 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.dis-nn < prev | next > new | recent | 2025-12 Change to browse by: cond-mat math math-ph math.MP quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation 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? ) 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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