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 Em-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 nD quantum liquids form a ∗-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.

Details

Title
Categories of quantum liquids I
Author
Kong, Liang 1 ; Zheng, Hao 2 

 Southern University of Science and Technology, Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China (GRID:grid.263817.9) (ISNI:0000 0004 1773 1790); International Quantum Academy, Shenzhen, China (GRID:grid.263817.9); Southern University of Science and Technology, Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Shenzhen, China (GRID:grid.263817.9) (ISNI:0000 0004 1773 1790) 
 Southern University of Science and Technology, Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China (GRID:grid.263817.9) (ISNI:0000 0004 1773 1790); Southern University of Science and Technology, Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Shenzhen, China (GRID:grid.263817.9) (ISNI:0000 0004 1773 1790); Tsinghua University, Institute for Applied Mathematics, Beijing, China (GRID:grid.12527.33) (ISNI:0000 0001 0662 3178); Beijing Institute of Mathematical Sciences and Applications, Beijing, China (GRID:grid.12527.33); Peking University, Department of Mathematics, Beijing, China (GRID:grid.11135.37) (ISNI:0000 0001 2256 9319) 
Pages
70
Publication year
2022
Publication date
Aug 2022
Publisher
Springer Nature B.V.
e-ISSN
10298479
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2848484317
Copyright
© The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.