Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
Abstract
We develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data.
Keywords
Cite
@article{arxiv.2409.05852,
title = {Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization},
author = {Yu Zhao and Yidun Wan},
journal= {arXiv preprint arXiv:2409.05852},
year = {2025}
}
Comments
4 Figures, 37 Pages. Version 2 has references added and typos corrected. arXiv admin note: text overlap with arXiv:2408.02664. Authors note: This article is a subsequent work following arXiv:2408.02664, with some overlapping TikZ commands and content included in the appendix. Proper attribution is provided, and this article offers new contributions in a different area