{"paper":{"title":"Translation invariant pure state on $\\otimes_{\\IZ}/!M_d(\\IC)$ and Haag duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Anilesh Mohari","submitted_at":"2013-09-29T15:19:05Z","abstract_excerpt":"We prove Haag duality property of any translation invariant pure state on $\\clb = \\otimes_{\\IZ}/!M_d(\\IC), \\;d \\ge 2$, where $/!M_d(\\IC)$ is the set of $d \\times d$ dimensional matrices over the field of complex numbers. We also prove a necessary and sufficient condition for a translation invariant factor state to be pure on $\\clb$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7607","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"}