Topological phase transition of deformed ${\mathbb Z}_3$ toric code
Summarize this article with:
Quantum Physics arXiv:2603.09107 (quant-ph) [Submitted on 10 Mar 2026] Title:Topological phase transition of deformed ${\mathbb Z}_3$ toric code Authors:Yun-Tak Oh, Hyun-Yong Lee View a PDF of the paper titled Topological phase transition of deformed ${\mathbb Z}_3$ toric code, by Yun-Tak Oh and 1 other authors View PDF HTML (experimental) Abstract:We investigate the topological phase transitions of the deformed $\mathbb{Z}_3$ toric code, constructed by applying local deformations to the $\mathbb{Z}_3$ cluster state followed by projective measurements. Using the loop-gas and net configuration framework, we map the wavefunction norm to classical partition functions: the $Q=3$ Potts model for single-parameter deformations and a novel $\mathbb{Z}_3$ generalization of the Ashkin-Teller model (AT$_3$) for the general two-parameter case. The phase diagram, obtained via the projected entangled pair state (PEPS) representation and the variational uniform matrix product state (VUMPS) method, exhibits three phases -- the toric code phase, an $e$-confined phase, and an $e$-condensed phase -- separated by critical lines with central charges $c=4/5$ ($\mathbb{Z}_3$ parafermion conformal field theory) and $c=8/5$, along with isolated antiferromagnetic critical points at $c=1$ ($\mathbb{Z}_4$ parafermion conformal field theory). At these critical points, the system reduces to a square ice model with an emergent $U(1)$ 1-form symmetry, exhibiting Hilbert space fragmentation and quantum many-body scar states. Unlike the $\mathbb{Z}_2$ case, the absence of a sign-change duality leads to a richer phase structure. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.09107 [quant-ph] (or arXiv:2603.09107v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.09107 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hyun-Yong Lee [view email] [v1] Tue, 10 Mar 2026 02:39:46 UTC (12,238 KB) Full-text links: Access Paper: View a PDF of the paper titled Topological phase transition of deformed ${\mathbb Z}_3$ toric code, by Yun-Tak Oh and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech 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?)