Long-range mutual information and topological uncertainty principle

Understand

Ordered phases in Landau paradigm can be diagnosed by a local order parameter, whereas topologically ordered phases cannot be detected in such a way.

• In this paper, we propose long-range mutual information(LRMI) as a unified diagnostic for both conventional long-range order and topological order.
• Using the LRMI, we characterize orders in $n+1$D gapped systems as $m$-membrane condensates with $ 0 \leq m \leq n-1$.
• The familiar conventional order and 2+1D topological orders are respectively identified as $0$-membrane and $1$-membrane condensates.