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 CFT-type 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 such that its monoidal center is trivial. We also study the categorical descriptions of the boundaries of these models. In the end, we obtain a classification of and the categorical descriptions of all 1-dimensional (spatial dimension) gapped quantum phases with a bosonic/fermionic finite onsite symmetry.
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Kong, L., Wen, XG. & Zheng, H. One dimensional gapped quantum phases and enriched fusion categories. J. High Energ. Phys. 2022, 22 (2022). https://doi.org/10.1007/JHEP03(2022)022
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DOI: https://doi.org/10.1007/JHEP03(2022)022