Categories of quantum liquids II

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 $\ge 3$.

35 pages. Final version

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Cited by in corpus (6)

• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Finite Semisimple Module 2-Categories
• Category of SET orders
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Generalized Landau Paradigm for quantum phases and phase transitions
• Tube Category, Tensor Renormalization and Topological Holography