Stability and Loop Models from Decohering Non-Abelian Topological Order

Understand

Decohering topological order (TO) is central to the many-body physics of open quantum matter and decoding transitions.

• We identify relevant statistical mechanical models for decohering non-Abelian TO, which have been crucial for understanding the error threshold of Abelian stabilizer codes.
• The decohered density matrix can be described by loop models, whose topological loop weight $N$ is given by the quantum dimension of the decohering anyon -- reducing to the Ising model if $N=1$.
• In particular, the R\'enyi-$n$ moments of the decohered state correspond to $n$ coupled O$(N)$ loop models, and we exactly diagonalize the density matrix at maximal error rate.