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.

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

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Cited by in corpus (1)

• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization