Self-dual Higgs transitions: Toric code and beyond

[2601.20945] Self-dual Higgs transitions: Toric code and beyond Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2601.20945 (cond-mat) [Submitted on 28 Jan 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Self-dual Higgs transitions: Toric code and beyond Authors: Wenjie Ji , Ryan A. Lanzetta , Zheng Zhou , Chong Wang View PDF HTML (experimental) Abstract: The toric code, when deformed in a way that preserves the self-duality $\mathbb{Z}_2$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the $\mathbb{Z}_2$ symmetry. Numerically, this transition was found to be continuous, which makes it particularly enigmatic given the longstanding absence of a continuum field-theoretic description. In this work we propose such a continuum field theory for the transition dubbed the $SO(4)_{2,-2}$ Chern-Simons-Higgs (CSH) theory. We show that our field theory provides a natural "mean-field" understanding of the phase diagram. Moreover, it can be generalized to an entire series of theories, namely the $SO(4)_{k,-k}$ CSH theories, labeled by an integer $k$. For each $k>2$, the theory describes an analogous transition involving different non-Abelian topological orders, such as the double Fibonacci order ($k=3$) and the $S_3$ quantum double ($k=4$). For $k=1$, we conjecture that the corresponding CSH transition is in fact infrared-dual to the $3d$ Ising transition, in close analogy with the particle-vortex duality of a complex scalar. Comments: 5+5 pages, published version Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th) Cite as: arXiv:2601.20945 [cond-mat.str-el] (or arXiv:2601.20945v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2601.20945 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Lett. 137, 086505 (2026) Related DOI : https://doi.org/10.1103/flfk-m8lj Focus to learn more DOI(s) linking to related resources Submission history From: Chong Wang [ view email ] [v1] Wed, 28 Jan 2026 19:00:04 UTC (67 KB) [v2] Tue, 25 Aug 2026 08:53:03 UTC (70 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 | 2026-01 Change to browse by: cond-mat cond-mat.stat-mech hep-th References & Citations INSPIRE HEP 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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