Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems

Condensed Matter > Strongly Correlated Electrons [Submitted on 3 Apr 2026] Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems Tsubasa Oishi, Hiromi Ebisu 't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by \sim a_1\wedge a_2\wedge a_3\wedge a_4, where the a_i denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter. Comments: 33 pages, 13 figures Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) Report number: YITP-26-31, RIKEN-iTHEMS-Report-26 Cite as: arXiv:2604.02856 [cond-mat.str-el]   (or arXiv:2604.02856v1 [cond-mat.str-el] for this version)   https://doi.org/10.48550/arXiv.2604.02856 Focus to learn more Submission history From: Tsubasa Oishi [view email] [v1] Fri, 3 Apr 2026 08:22:30 UTC (237 KB) Access Paper: HTML (experimental) view license Current browse context: cond-mat.str-el < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat hep-th quant-ph 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)