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Categories of quantum liquids II
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abstract
We continue to develop the theory of separable higher categories, including center functors, higher centralizers, modular extensions and group theoretical higher fusion categories. Moreover, we outline a theory of orthogonal higher categories to treat anti-unitary symmetries. Using these results we derive a systematic classification of gapped quantum liquids and predict many new SPT orders in spacetime dimension $\ge3$.
Forward citations
Cited by 3 Pith papers
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Classification of symmetric fusion categories over $\mathbb{R}$
Every symmetric fusion category over R is equivalent to the semi-linear super representation category of a Z2-graded finite super group.
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Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d
Strange correlators and string order parameters for non-invertible SPT phases in 1+1d are systematically constructed from the interface algebra, giving local detectors of these phases.
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Tube Category, Tensor Renormalization and Topological Holography
For any rigid monoidal category C, the representations of the coend-defined tube category XC are equivalent to the relative center of the Yoneda embedding, with the Drinfeld center Z(C) embedded inside.
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