One dimensional gapped quantum phases and enriched fusion categories

@article{Kong2022OneDG,
  title={One dimensional gapped quantum phases and enriched fusion categories},
  author={Liang Kong and Xiao-Gang Wen and Hao Zheng},
  journal={Journal of High Energy Physics},
  year={2022}
}
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… 
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