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Categories of quantum liquids I
- Source :
- Journal of High Energy Physics
- Publication Year :
- 2022
- Publisher :
- Springer, 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 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.<br />36 pages, final version to appear in JHEP
- Subjects :
- High Energy Physics - Theory
Condensed Matter - Strongly Correlated Electrons
Nuclear and High Energy Physics
High Energy Physics - Theory (hep-th)
Strongly Correlated Electrons (cond-mat.str-el)
Mathematics::Category Theory
Mathematics - Quantum Algebra
FOS: Mathematics
Quantum Algebra (math.QA)
FOS: Physical sciences
Category Theory (math.CT)
Mathematics - Category Theory
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....06b1997ddac4e3b03f9d440d8d2cfecb