The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities

[2412.18504] The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2412.18504 (cond-mat) [Submitted on 24 Dec 2024 ( v1 ), last revised 11 Feb 2026 (this version, v5)] Title: The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities Authors: Naoto Shiraishi , Hal Tasaki View a PDF of the paper titled The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities, by Naoto Shiraishi and Hal Tasaki View PDF HTML (experimental) Abstract: We study the $S=\frac{1}{2}$ quantum spin system on the $d$-dimensional hypercubic lattice with $d\ge2$ with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently developed for quantum spin chains, we prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian. This result strongly suggests that the model is non-integrable. We note that our result applies to the XX model without a magnetic field, which is one of the easiest solvable models in one dimension. Comments: This is the final version, in which references were updated, and cosmetic changes were made to the Appendix. 40 pages, 9 figures. There are a 23-minute video that discusses the main results of the present work this https URL and a 44-minute video that explains the basic ideas of the proof this https URL Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2412.18504 [cond-mat.stat-mech] (or arXiv:2412.18504v5 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2412.18504 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Ann. Henri Poincaré (2026) Related DOI : https://doi.org/10.1007/s00023-026-01699-8 Focus to learn more DOI(s) linking to related resources Submission history From: Hal Tasaki [ view email ] [v1] Tue, 24 Dec 2024 15:42:23 UTC (878 KB) [v2] Mon, 30 Dec 2024 05:32:07 UTC (878 KB) [v3] Fri, 14 Feb 2025 02:34:12 UTC (926 KB) [v4] Sun, 9 Mar 2025 06:17:20 UTC (925 KB) [v5] Wed, 11 Feb 2026 08:36:56 UTC (927 KB) Full-text links: Access Paper: View a PDF of the paper titled The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities, by Naoto Shiraishi and Hal Tasaki View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2024-12 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 Loading... BibTeX formatted citation × loading... 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