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Non-invertible and higher-form symmetries in 2+1d lattice gauge theories

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arxiv 2405.13105 v1 pith:PGMWID5E submitted 2024-05-21 cond-mat.str-el hep-thquant-ph

Yichul Choi , Yaman Sanghavi , Shu-Heng Shao , Yunqin Zheng This is my paper
classification cond-mat.str-elhep-thquant-ph
keywords non-invertiblesymmetrylatticemodelsymmetriesanomalygaugestate
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abstract

We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the phase diagram, consistent with the "Higgs=SPT" proposal. Finally, we discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals

    cond-mat.str-el 2026-07 accept novelty 7.0 of 10

    In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.

  2. Disjoint additivity and local quantum physics

    hep-th 2025-09 conditional novelty 7.0 of 10

    Local quantum systems should obey disjoint additivity plus Haag duality, a combination that survives higher-form symmetries and fails for known nonlocal constructions.

  3. Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

    hep-th 2025-07 conditional novelty 7.0 of 10

    A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.

  4. Non-invertible translation from Lieb-Schultz-Mattis anomaly

    cond-mat.str-el 2026-01 conditional novelty 6.0 of 10

    Gauging the full internal symmetry of a lattice system with an LSM anomaly turns lattice translation into a non-invertible operator whose fusion rules involve condensation defects.

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