A topological phase transition on the edge of the 2d $\mathbb{Z}_2$ topological order

Understand

The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors.

• It provides a powerful tool to study pure edge topological phase transitions on the edges of 2d topological orders (without altering the bulks).
• In particular, it implies that the critical points are described by enriched fusion categories.
• In this work, we illustrate this idea in a concrete example: the 2d $\mathbb{Z}_2$ topological order.