One dimensional gapped quantum phases and enriched fusion categories

Abstract

In this work, we use Ising chain and Kitaev chain to check the validity of an earlier proposal in arXiv:2011.02859 that enriched fusion (higher) categories provide a unified categorical description of all gapped/gapless quantum liquid phases, including symmetry-breaking phases, topological orders, SPT/SET orders and certain gapless quantum phases. In particular, we show explicitly that, in each gapped phase realized by these two models, the spacetime observables form a fusion category enriched in a braided fusion category. We also study the categorical descriptions of the boundaries of these models. In the end, we provide a classification of and the categorical descriptions of all 1-dimensional (the spatial dimension) gapped quantum phases with a finite onsite symmetry.

27 pages. We add some remarks and references

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Cited by in corpus (20)

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• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Non-invertible topological defects in 4-dimensional ${\mathbb{Z}}_2$ pure lattice gauge theory
• Quantum Current and Holographic Categorical Symmetry
• Symmetry fractionalization and duality defects in Maxwell theory
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Fusion of one-dimensional gapped phases and their domain walls
• Enriched monoidal categories I: centers
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
• Generalized Landau Paradigm for quantum phases and phase transitions
• von Neumann Subfactors and Non-invertible Symmetries
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Tube Category, Tensor Renormalization and Topological Holography
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Condensation Completion and Defects in 2+1D Topological Orders