(2+1)d lattice models and tensor networks for gapped phases with categorical symmetry, by Kansei Inamura, Sheng-Jie Huang, Apoorv Tiwari, Sakura Schäfer-Nameki

SciPost Physics Home Authoring Refereeing Submit a manuscript About (2+1)d lattice models and tensor networks for gapped phases with categorical symmetry Kansei Inamura, Sheng-Jie Huang, Apoorv Tiwari, Sakura Schäfer-Nameki SciPost Phys. 20, 043 (2026) · published 13 February 2026 doi: 10.21468/SciPostPhys.20.2.043 pdf BiBTeX RIS Submissions/Reports Abstract Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach [L. Bhardwaj et al., SciPost Phys. 19, 056 (2025); L. Bhardwaj et al., arXiv: 2502.20440]. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider "all-boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups $G$ (possibly with an 't Hooft anomaly) via generalized gauging—that is, by stacking with an $H$-symmetric TFT and gauging a subgroup $H$. The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.2.043TI - (2+1)d lattice models and tensor networks for gapped phases with categorical symmetryPY - 2026/02/13UR - https://scipost.org/SciPostPhys.20.2.043JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 2SP - 043A1 - Inamura, KanseiAU - Huang, Sheng-JieAU - Tiwari, ApoorvAU - Schäfer-Nameki, SakuraAB - Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach [L. Bhardwaj et al., SciPost Phys. 19, 056 (2025); L. Bhardwaj et al., arXiv: 2502.20440]. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider "all-boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups $G$ (possibly with an 't Hooft anomaly) via generalized gauging—that is, by stacking with an $H$-symmetric TFT and gauging a subgroup $H$. The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples.ER - × @Article{10.21468/SciPostPhys.20.2.043, title={{(2+1)d lattice models and tensor networks for gapped phases with categorical symmetry}}, author={Kansei Inamura and Sheng-Jie Huang and Apoorv Tiwari and Sakura Schäfer-Nameki}, journal={SciPost Phys.}, volume={20}, pages={043}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.2.043}, url={https://scipost.org/10.21468/SciPostPhys.20.2.043},} Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Kansei Inamura, 2 Sheng-Jie Huang, 3 Apoorv Tiwari, 2 Sakura Schäfer-Nameki 1 Rudolf Peierls Centre for Theoretical Physics 2 University of Oxford 3 Syddansk Universitet / University of Southern Denmark [SDU] Funders for the research work leading to this publication Engineering and Physical Sciences Research Council [EPSRC] European Research Council [ERC] Leverhulme Trust National Science Foundation [NSF] UK Research and Innovation Villum Fonden / Velux Foundation