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A bstract 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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Universal entanglement signatures of foliated fracton phases
Fracton models exhibit a variety of exotic properties and lie beyondthe conventional framework of gapped topological order. In , wegeneralized the notion of gapped phase to one of foliatedfracton phase by allowing the addition of layers of gappedtwo-dimensional resources in the adiabatic evolution between gappedthree-dimensional models. Moreover, we showed that the X-cube model is afixed point of one such phase. In this paper, according to thisdefinition, we look for universal properties of such phases which remaininvariant throughout the entire phase. We propose multi-partiteentanglement quantities, generalizing the proposal of topologicalentanglement entropy designed for conventional topological phases. Wepresent arguments for the universality of these quantities and show thatthey attain non-zero constant value in non-trivial foliated fractonphases.
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- Award ID(s):
- 1654340
- PAR ID:
- 10134737
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 6
- Issue:
- 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.6.1.015
