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Categorical Landau Paradigm: Phases, Transitions and Lattice Models

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If you have a question about this talk, please contact Gaurav .

I will introduce a framework based on Symmetry Topological Field Theory (SymTFT) for characterizing and classifying both gapped and gapless phases, as well as phase transitions in quantum systems with global categorical symmetries. This characterization will be expressed in terms of sets of condensed, confined, and deconfined generalized symmetry charges, evoking concepts familiar from superconductivity. Furthermore, I will demonstrate how the SymTFT data can be transformed into an ultraviolet (UV) lattice model—such as an anyon chain model in 1+1 dimensions or a fusion surface model in 2+1 dimensions—that realizes these phases and transitions in the infrared (IR) limit.

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