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. The Kogut-Susskind lattice gauge theory model is a special case of our model if the full degrees of freedom of the model are truncated from SU(2) representations to quantum group SU(2)_k. 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.