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

TL;DR

This paper introduces a detailed string-net model framework for realizing and classifying bosonic anyon condensation in 2+1D topological orders, providing a microscopic and computational approach.

Contribution

It develops a Hamiltonian-based method to realize and classify all bosonic anyon condensations within string-net models, offering a microscopic and algorithmic perspective.

Findings

Classifies all bosonic anyon condensations in string-net models

Constructs Hamiltonians bridging parent and child topological orders

Provides algorithms for calculating categorical data of anyon condensation

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.