Phase diagram of the Kitaev-Heisenberg-$Γ$ model: Classical and quantum magnetism, frustration, and subdominant interactions

[2606.13263] Phase diagram of the Kitaev-Heisenberg-$Γ$ model: Classical and quantum magnetism, frustration, and subdominant interactions Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2606.13263 (cond-mat) [Submitted on 11 Jun 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Phase diagram of the Kitaev-Heisenberg-$Γ$ model: Classical and quantum magnetism, frustration, and subdominant interactions Authors: Kiyu Fukui , Yukitoshi Motome View PDF HTML (experimental) Abstract: The Kitaev spin liquid provides a rare example of exactly solvable quantum spin liquid states. Intensive research over the past two decades has identified a variety of its candidate materials. In real materials, however, the Kitaev interaction is inevitably accompanied by additional magnetic interactions such as the Heisenberg and $\Gamma$ interactions. These interactions often induce magnetic ordering at low temperatures, making it essential to clarify their effects in the search for and design of Kitaev spin liquid candidate materials. In this study, we revisit the ground-state phase diagram of the Kitaev-Heisenberg-$\Gamma$ model from both classical and quantum perspectives, using state-of-the-art numerical techniques. In the classical case, we reveal a $zoo$ $of$ $noncollinear$ $orders$, where a variety of noncollinear multiple-$Q$ magnetic orders with and without incommensurate modulations emerge. In the quantum case, we unravel that quantum fluctuations suppress many of the competing orders found in the classical case, resulting in a reduced number of dominant incommensurate orders. We further identify $highly$ $frustrated$ regions, where spiral spin liquid states as well as new magnetically ordered states are potentially stabilized by other additional magnetic interactions. Our results provide a comprehensive perspective on the Kitaev-Heisenberg-$\Gamma$ model for both classical and quantum spins and offer a valuable guide not only for interpreting experimental results on candidate materials, but also for searching and designing new materials to realize the Kitaev spin liquid. Comments: 19 pages, 13 figures Subjects: Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2606.13263 [cond-mat.str-el] (or arXiv:2606.13263v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2606.13263 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 114, 074429 (2026) Related DOI : https://doi.org/10.1103/rbrl-6shw Focus to learn more DOI(s) linking to related resources Submission history From: Kiyu Fukui [ view email ] [v1] Thu, 11 Jun 2026 12:19:53 UTC (6,553 KB) [v2] Tue, 25 Aug 2026 02:55:10 UTC (6,622 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 | 2026-06 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. 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