Categories of quantum liquids I

Kong，Liang1,2,3; Zheng，Hao1,3,4,5,6

2022-08-01

10.1007/JHEP08(2022)070

Journal of High Energy Physics   Impact Factor & Quartile

1029-8479

1029-8479

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-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.

Anyons Topological Field Theories Topological States of Matter

SCI

English

NI Journal Papers

First ; Corresponding

Physics

Physics, Particles & Fields

WOS:000836610800015

SPRINGER

PHYSICS

2-s2.0-85135446829

Scopus

1.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
2.International Quantum Academy,Shenzhen,518048,China
3.Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
4.Institute for Applied Mathematics,Tsinghua University,Beijing,100084,China
5.Beijing Institute of Mathematical Sciences and Applications,Beijing,101408,China
6.Department of Mathematics,Peking University,Beijing,100871,China

Kong，Liang,Zheng，Hao. Categories of quantum liquids I[J]. Journal of High Energy Physics,2022,2022(8).

Kong，Liang,&Zheng，Hao.(2022).Categories of quantum liquids I.Journal of High Energy Physics,2022(8).

Kong，Liang,et al."Categories of quantum liquids I".Journal of High Energy Physics 2022.8(2022).