2024/03/28 by Rongge Xu, Xu, Rongge, Holiverse Yang +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2403.19779
openalex publication_date 2024/03/28 · openalex created_date 2024/04/03 · openalex updated_date 2026/07/28
We classify E2 condensable algebras in a modular tensor category C up to 2-Morita equivalence. From a physical perspective, this is equivalent to providing a criterion for when different E2 condensable algebras result in the same condensed topological phase in a 2d anyon condensation process. By considering the left and right centers of E1 condensable algebras in C, we exhaust all 2-Morita equivalent E2 condensable algebras in C and provide a method to recover E1 condensable algebras from 2-Morita equivalent E2 condensable algebras. We also prove that intersecting Lagrangian algebras in C \boxtimes C with its left and right components generates all 2-Morita equivalent E2 condensable algebras in C. This paper establishes a complete interplay between E1 condensable algebras in C, 2-Morita equivalent E2 condensable algebras in C, and Lagrangian algebras in C \boxtimes C. The relations between different condensable algebras can be translated into their module categories, which correspond to domain walls in topological orders. We introduce a two-step condensation process and study the fusion of domain walls. We also show that an automorphism of an E2 condensable algebra may lead to a nontrivial braided autoequivalence in the condensed phase. As concrete examples, we interpret the categories of quantum doubles of finite groups. We also discuss examples beyond group symmetries. Moreover, our results can be generalized to Witt-equivalent modular tensor categories.