# 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…

## 5 Citations

Categorical descriptions of 1-dimensional gapped phases with abelian onsite symmetries

- Physics, Mathematics
- 2022

In a recent work arXiv:2108.08835, Kong, Wen and Zheng use Ising chain and Kitaev chain to show that the macroscopic observables in a 1d (space dimension) gapped quantum phase form an enriched fusion…

Non-invertible topological defects in 4-dimensional Z2 pure lattice gauge theory

- Materials Science
- 2021

We explore topological defects in the 4-dimensional pure Z2 lattice gauge theory. This theory has 1-form Z2 center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW…

Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

- Materials Science
- 2021

We explore topological defects in the 4-dimensional pure Z2 lattice gauge theory. This theory has 1-form Z2 center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW…

Algebra of local symmetric operators and braided fusion $n$-category -- symmetry is a shadow of topological order

- Mathematics
- 2022

Symmetry is usually deﬁned via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of…

Categories of quantum liquids I

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd’s work on condensation completion. Based on this theory, we prove some fundamental results…

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