ﻻ يوجد ملخص باللغة العربية
We develop the mathematical theory of separable and unitary $n$-categories based on Gaiotto and Johnson-Freyds theory of condensation completion. We use it to study the categories of topological orders by including gapless quantum phases and defects. In particular, we show that all the topological features of a potentially gapless quantum phase can be captured by its topological skeleton, and that the category of the topological skeletons of higher dimensional gapped/gapless quantum phases can be explicitly computed categorically from a simple coslice 1-category.
In this second part of a series work, we further develop the theory of higher fusion categories, including center functors, centralizers and group theoretic higher fusion categories. Along the way we prove several conjectures on modular extensions an
We construct a state-sum type invariant of smooth closed oriented $4$-manifolds out of a $G$-crossed braided spherical fusion category ($G$-BSFC) for $G$ a finite group. The construction can be extended to obtain a $(3+1)$-dimensional topological qua
Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carryin
Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation o
When studying quantum field theories and lattice models, it is often useful to analytically continue the number of field or spin components from an integer to a real number. In spite of this, the precise meaning of such analytic continuations has nev