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arXiv · 2108.08835

One dimensional gapped quantum phases and enriched fusion categories

Liang Kong·Xiao-Gang Wen·Hao Zheng
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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.

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Liang Kong, Xiao-Gang Wen, Hao Zheng. 2021-08-19. One dimensional gapped quantum phases and enriched fusion categories. https://doi.org/10.1007/jhep03(2022)022

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