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Illustrating the Categorical Landau Paradigm in Lattice Models

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arxiv 2405.05302 v2 pith:3BUUQIXP submitted 2024-05-08 cond-mat.str-el hep-thmath-phmath.MP

classification cond-mat.str-elhep-thmath-phmath.MP
keywords non-invertiblesymmetriessymmetrycategoricallandaulatticeparadigmbreaking
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Recent years have seen the concept of global symmetry extended to non-invertible (or categorical) symmetries, for which composition of symmetry generators is not necessarily invertible. Such non-invertible symmetries lead to a generalization of the standard Landau paradigm. In this work we substantiate this framework by providing a (1+1)d lattice model, whose gapped phases and phase transitions can only be explained by symmetry breaking of non-invertible symmetries.

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Cited by 3 Pith papers

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

  1. Symmetry TFTs for Continuous Spacetime Symmetries

    hep-th 2025-09 conditional novelty 7.0 of 10

    Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.

  2. SymTFT Approach for Mixed States with Non-Invertible Symmetries

    quant-ph 2025-07 conditional novelty 7.0 of 10

    A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.

  3. A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT

    cond-mat.str-el 2025-06 conditional novelty 7.0 of 10

    Competing anyon condensates in string-net models generate critical lattice models, including new Haagerup-symmetric CFT candidates with central charges near 1.3, 1.8 and 2.5.

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