Nonabelian Anyon Condenstion in 2+1d topological orders: A String-Net Model Realization

Yu Zhao, Yidun Wan
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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.
2+1d 拓扑阶中的非阿贝尔安永共轭:弦网模型的实现
我们建立了一个在弦网模型中实现拓扑阶任子凝聚的综合框架,方法是构建一个哈密顿,在任子凝聚前的母弦网模型和任子凝聚后的子弦网模型之间架起桥梁。我们的方法对任何母弦网模型中所有可能的玻色子凝聚类型进行了分类,并确定了相应子模型中的基本自由度。与传统的 UMTC 拓扑阶次视角相比,我们的方法在微观层面提供了对玻色子凝聚的精细分类描述。我们还通过基于模型的物理量,明确表示了表征任子凝聚的相关 UMTC 分类实体,并提供了计算这些分类数据的实用算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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