One dimensional gapped quantum phases and enriched fusion categories
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Author(s)
Kong, Liang
Wen, Xiao-Gang
Zheng, Hao
Date Issued
March 3, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 Mar 03;2022(3):22
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP03(2022)022
