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.
Keywords
Cite
@article{arxiv.2108.08835,
title = {One dimensional gapped quantum phases and enriched fusion categories},
author = {Liang Kong and Xiao-Gang Wen and Hao Zheng},
journal= {arXiv preprint arXiv:2108.08835},
year = {2022}
}
Comments
27 pages. We add some remarks and references