{"paper":{"title":"Matrix formulation for non-Abelian families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Tian Lan","submitted_at":"2019-08-07T12:46:31Z","abstract_excerpt":"We generalize the $K$ matrix formulation to non-trivial non-Abelian families of 2+1D topological orders. Given a topological order $\\mathcal C$, any topological order in the same non-Abelian family as $\\mathcal C$ can be efficiently described by $\\boldsymbol{a}=(a_I)$ where $a_I$ are Abelian anyons in $\\mathcal C$, together with a symmetric invertible matrix $K$, $K_{IJ}=k_{IJ}-t_{a_I,a_J}$ where $k_{IJ}$ are integers, $k_{II}$ are even and $t_{a_I,a_J}$ are the mutual statistics between $a_I,a_J$. In particular, when $\\mathcal C$ is a root whose rank is the smallest in the family, $K$ becomes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02599","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02599/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}