Statistics as a local phase: crystalline order and quench dynamics of emergent dimers in Ising gauge theories

[2608.26264] Statistics as a local phase: crystalline order and quench dynamics of emergent dimers in Ising gauge theories Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2608.26264 (cond-mat) [Submitted on 26 Aug 2026 ( v1 ), last revised 10 Oct 2026 (this version, v2)] Title: Statistics as a local phase: crystalline order and quench dynamics of emergent dimers in Ising gauge theories Authors: Umberto Borla , Riccardo Cioli , Jad C. Halimeh View PDF HTML (experimental) Abstract: How does the Bose or Fermi statistics of microscopic particles survive when confinement binds them into emergent bosonic composites? We address this question in the strong-coupling limit of a $2+1$D $\mathbb{Z}_2$ lattice gauge theory, where charges are confined into tightly bound pairs that can be described by an effective dimer model. We find that the statistics of the underlying matter is encoded entirely in a single local hopping phase $\varphi$ -$0$ for bosons, $\pi$ for fermions. Treating $\varphi$ as a continuous parameter that interpolates between the two, we map the ground-state phase diagram with the help of tensor-network methods. The angle $\varphi$ itself drives a transition between a dimer-superfluid and a dimer-charge density wave state, while the magnetic coupling binds neighboring dimers into resonating pairs, in competition with the inter-dimer repulsion. We identify a novel gapped phase in which dimer pairs crystallize into an ordered pattern of resonating plaquettes. Finally, we propose a quench protocol under which identical dimer configurations evolve in markedly different ways depending on the statistics of their constituents. This provides a dynamical probe of the internal structure of dimers, and allows to detect ordered phases through real-time signatures, within reach of simulators that natively realize bosonic degrees of freedom. Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph) Cite as: arXiv:2608.26264 [cond-mat.str-el] (or arXiv:2608.26264v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2608.26264 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Umberto Borla [ view email ] [v1] Wed, 26 Aug 2026 18:00:07 UTC (819 KB) [v2] Sat, 10 Oct 2026 12:07:58 UTC (1,060 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 | 2026-08 Change to browse by: cond-mat cond-mat.quant-gas quant-ph 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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