Anyon condensation in mixed-state topological order

TL;DR

This paper explores the process of anyon condensation in mixed-state topological orders, extending the theory to include non-invertible anyons and multiple condensations, with implications for classifying phases and understanding topological invariants.

Contribution

It introduces a comprehensive framework for anyon condensation in mixed states, including non-invertible anyons and successive condensations, and clarifies conditions for resulting pure-state orders.

Findings

Condensable anyons correspond to connected étale algebras.

Methods for generic anyon condensation including non-invertible cases.

Some condensations produce pure-state topological orders.

Abstract

We discuss anyon condensation in mixed-state topological order. The phases were recently conjectured to be classified by pre-modular fusion categories. Just like anyon condensation in pure-state topological order, a bootstrap analysis shows condensable anyons are given by connected \'etale algebras. We explain how to perform generic anyon condensation including non-invertible anyons and successive condensations. Interestingly, some condensations lead to pure-state topological orders. We clarify when this happens. We also compute topological invariants of equivalence classes.