154 citations · 332 across the 13 of their papers we have counts for
7 papers · 1 filter
Higher condensation theory
Liang Kong, Zhi-Hao Zhang, Jiaheng Zhao +1
We develop a unified mathematical theory of defect condensations for topological orders in all dimensions based on higher categories, higher algebras and higher representations. A…
String Condensations in 3+1D and Lagrangian Algebras
Jiaheng Zhao, Jia-Qi Lou, Zhi-Hao Zhang +3
We present three Lagrangian algebras in the modular 2-category associated to the 3+1D topological order and discuss their physical interpretations, connecting algebr…
An invitation to topological orders and category theory
Liang Kong, Zhi-Hao Zhang
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for stude…
Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
Rongge Xu, Zhi-Hao Zhang
In this work, we analyze the macroscopic observables in the 1+1D gapped phases with Abelian onsite symmetries and show that the spacetime observables for each gapped phase form a c…
Defects in the 3-dimensional toric code model form a braided fusion 2-category
Liang Kong, Yin Tian, Zhi-Hao Zhang
It was well known that there are -particles and -strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional topologica…
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
Liang Kong, Tian Lan, Xiao-Gang Wen +2
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in…
Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
Wenjie Xi, Zhi-Hao Zhang, Zheng-Cheng Gu +1
Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian syst…