154 citations · 332 across the 13 of their papers we have counts for
13 papers
Classification of symmetric fusion categories over
Mo Huang, Hao Xu, Zhi-Hao Zhang
We show that every symmetric fusion category over is equivalent to the category of finite-dimensional semi-linear representations of a -graded finite sup…
LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories)
Rongge Xu, Hui Dai, Yiming Fu +5
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -…
The 2-character theory of finite 2-groups
Mo Huang, Hao Xu, Zhi-Hao Zhang
We generalize the notion of character for 2-representations of finite 2-groups. The properties of 2-characters bear strong similarities to those classical characters of finite grou…
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…
Tannaka-Krein duality for finite 2-groups
Mo Huang, Zhi-Hao Zhang
Let be a finite 2-group. We show that the 2-category of finite semisimple 2-representations is a symmetric fusion 2-category. We also rel…
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…
Enriched monoidal categories I: centers
Liang Kong, Wei Yuan, Zhi-Hao Zhang +1
This work is the first one in a series, in which we develop a mathematical theory of enriched (braided) monoidal categories and their representations. In this work, we introduce th…
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 with finite internal symmetries in all dimensions
Liang Kong, Tian Lan, Xiao-Gang Wen +2
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approach…
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…