Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models

[2605.22908] Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2605.22908 (cond-mat) [Submitted on 21 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models Authors: Pedro M. Cônsoli , Aayush Vijayvargia , Onur Erten View PDF HTML (experimental) Abstract: We propose a family of layered quantum spin-orbital models as a platform to study fractionalization, unconventional forms of symmetry-breaking order, and their possible coexistence. The models are built by stacking $N$ layers of a square-lattice system in which Kitaev-type interactions promote the formation of a $\mathbb{Z}_2$ quantum spin-orbital liquid and coupling the different layers via Ising spin interactions. Using a parton construction, we show how, at low energies, these Hamiltonians can be mapped to $N$-component Fermi Hubbard models on a $\pi$-flux square lattice at half filling. We also demonstrate that the models acquire an emergent SU($N$) symmetry in the limit of equal all-to-all interlayer couplings and argue that, for $N>2$, the proximity to this limit offers the potential to realize an array of competing phases. To illustrate this point, we compute the zero-temperature phase diagram of the effective $N=3$ Hubbard model within mean-field theory and uncover rich phenomena, including intertwined orders and flavor-selective localization. Mapping back to the original degrees of freedom reveals that the ground states realize distinct forms of magnetic fragmentation, wherein the orbitals remain in a quantum liquid state whereas the spins can present conventional long-range order or nonlocal order characterized by a nontrivial string order parameters. We highlight possible extensions of our construction as well as its potential to provide concrete microscopic models for different fractionalized quantum critical points. Comments: 11+5 pages, 5 figures; v2. Minor changes, published version Subjects: Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2605.22908 [cond-mat.str-el] (or arXiv:2605.22908v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2605.22908 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 114, 115106 (2026) Related DOI : https://doi.org/10.1103/3xmh-cb7b Focus to learn more DOI(s) linking to related resources Submission history From: Pedro Cônsoli [ view email ] [v1] Thu, 21 May 2026 18:00:28 UTC (3,259 KB) [v2] Thu, 27 Aug 2026 20:10:37 UTC (3,259 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2026-05 Change to browse by: cond-mat References & Citations SciX 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)

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