{"paper":{"title":"Long-range mutual information and topological uncertainty principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Chao-Ming Jian, Isaac H. Kim, Xiao-Liang Qi","submitted_at":"2015-08-27T20:13:10Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07006","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}