Graph-theoretical search for integrable multistate Landau-Zener models
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Quantum Physics arXiv:2512.15046 (quant-ph) [Submitted on 17 Dec 2025] Title:Graph-theoretical search for integrable multistate Landau-Zener models Authors:Zixuan Li, Chen Sun View a PDF of the paper titled Graph-theoretical search for integrable multistate Landau-Zener models, by Zixuan Li and Chen Sun View PDF HTML (experimental) Abstract:The search for exactly solvable models is an evergreen topic in theoretical physics. In the context of multistate Landau-Zener models -- $N$-state quantum systems with linearly time-dependent Hamiltonians -- the theory of integrability provides a framework for identifying new solvable cases. In particular, it was proved that the integrability of a specific class known as the multitime Landau-Zener (MTLZ) models guarantees their exact solvability. A key finding was that an $N$-state MTLZ model can be represented by data defined on an $N$-vertex graph. While known host graphs for MTLZ models include hypercubes, fans, and their Cartesian products, no other families have been discovered, leading to the conjecture that these are the only possibilities. In this work, we conduct a systematic graph-theoretical search for integrable models within the MTLZ class. By first identifying minimal structures that a graph must contain to host an MTLZ model, we formulate an efficient algorithm to systematically search for candidate graphs for MTLZ models. Implementing this algorithm using computational software, we enumerate all candidate graphs with up to $N = 13$ vertices and perform an in-depth analysis of those with $N \le 11$. Our results corroborate the aforementioned conjecture for graphs up to $11$ vertices. For even larger graphs, we propose a specific family, termed descendants of ``$(0,2)$-graphs'', as promising candidates that may violate the conjecture above. Our work can serve as a guideline to identify new exactly solvable multistate Landau-Zener models in the future. Comments: Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Combinatorics (math.CO); Exactly Solvable and Integrable Systems (nlin.SI) Cite as: arXiv:2512.15046 [quant-ph] (or arXiv:2512.15046v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.15046 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Chen Sun [view email] [v1] Wed, 17 Dec 2025 03:22:17 UTC (1,026 KB) Full-text links: Access Paper: View a PDF of the paper titled Graph-theoretical search for integrable multistate Landau-Zener models, by Zixuan Li and Chen SunView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.mes-hall math math-ph math.CO math.MP nlin nlin.SI 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?)