Reflections on time-reversal in the Symmetry Topological Field Theory

[2603.26884] Reflections on time-reversal in the Symmetry Topological Field Theory Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2603.26884 (cond-mat) [Submitted on 27 Mar 2026 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Reflections on time-reversal in the Symmetry Topological Field Theory Authors: Lea E. Bottini , Nick G. Jones View PDF HTML (experimental) Abstract: Symmetry under time-reversal appears in the microscopic description of many physical systems. In a quantum mechanical setting it acts as an anti-unitary operator, so does not fall under general analyses based on unitary symmetries. In classifying zero temperature phases of matter in (1+1)d lattice models, the role of anti-unitary symmetries is, however, well-understood. In recent years, the Symmetry Topological Field Theory (SymTFT) approach to this classification has given a general framework to understand symmetries as topological defects, but does not naturally include anti-unitary symmetries. Following recent proposals in the literature, we adopt a symmetry-enriched SymTFT for a theory with both internal and time-reversal symmetry. In particular, we take a standard SymTFT associated with an internal unitary symmetry that is then enriched by a background time-reversal symmetry. A detailed analysis of the topological boundary conditions of this enriched SymTFT allows us to characterize the corresponding (1+1)d gapped phases that preserve the enriching symmetry (i.e. those that do not spontaneously break this symmetry in the ground state). Line operators in the SymTFT approach are related to non-local string-order parameters (with charged end-point operators) for SPT phases. These are subtle in the anti-unitary case and we explore them both on the lattice and in the continuum. We include an analysis of unitary string order parameters that reveal the Klein bottle SPT invariant. On the lattice, we show that the correct end-point charge coincides with the time-reversal-charge only when the end-point operator is hermitian. Comments: v2 close to published version Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.26884 [cond-mat.str-el] (or arXiv:2603.26884v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2603.26884 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SciPost Phys. Core 9, 050 (2026) Related DOI : https://doi.org/10.21468/SciPostPhysCore.9.3.050 Focus to learn more DOI(s) linking to related resources Submission history From: Nick Jones [ view email ] [v1] Fri, 27 Mar 2026 18:02:24 UTC (932 KB) [v2] Mon, 24 Aug 2026 19:03:11 UTC (924 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 | 2026-03 Change to browse by: cond-mat hep-th References & Citations INSPIRE HEP NASA ADS 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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