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arXiv · 1508.07006

Long-range mutual information and topological uncertainty principle

Chao-Ming Jian·Isaac H. Kim·Xiao-Liang Qi
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Abstract

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. We propose and study the topological uncertainty principle, which describes the non-commuting nature of non-local order parameters in topological orders.

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Chao-Ming Jian, Isaac H. Kim, Xiao-Liang Qi. 2015-09-10. Long-range mutual information and topological uncertainty principle. https://arxiv.org/abs/1508.07006

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