Categories of quantum liquids I

Liang Kong; Hao Zheng

doi:10.1007/jhep08(2022)070

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arXiv · 2011.02859

Categories of quantum liquids I

Liang Kong·Hao Zheng

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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 on $E_m$-multi-fusion higher categories and their higher centers. We also outline a theory of unitary higher categories based on a $*$-version of condensation completion. After these mathematical preparations, based on the idea of topological Wick rotation, we develop a unified mathematical theory of all quantum liquids, which include topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like gapless phases. We explain that a quantum liquid consists of two parts, the topological skeleton and the local quantum symmetry, and show that all $n$D quantum liquids form a $*$-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.

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Liang Kong, Hao Zheng. 2020-11-05. Categories of quantum liquids I. https://doi.org/10.1007/jhep08(2022)070

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