{"paper":{"title":"Topologically Ordered Steady States in Open Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Steady-state topological degeneracy in open quantum systems is stable in three dimensions but fragile in two.","cross_cats":["cond-mat.mes-hall","cond-mat.quant-gas","cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"He-Ran Wang, Xu-Dong Dai, Zhong Wang, Zijian Wang","submitted_at":"2023-06-21T18:00:09Z","abstract_excerpt":"The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, w"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The two representative Liouvillians constructed via engineered dissipation admit exact solutions whose steady states carry the claimed topological degeneracy (abstract, paragraph 2).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Steady-state topological degeneracy in open quantum systems is stable in three dimensions but fragile in two.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cc8fda04473fea957c58e429a323ff0e7fb54c837d5dc91a4b28b8472150e692"},"source":{"id":"2306.12482","kind":"arxiv","version":2},"verdict":{"id":"111d2666-4309-44f5-9610-a3188d131b39","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T07:48:53.288817Z","strongest_claim":"while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized","one_line_summary":"Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The two representative Liouvillians constructed via engineered dissipation admit exact solutions whose steady states carry the claimed topological degeneracy (abstract, paragraph 2).","pith_extraction_headline":"Steady-state topological degeneracy in open quantum systems is stable in three dimensions but fragile in two."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.12482/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":44,"sample":[{"doi":"","year":null,"title":"Contrary to L0, L† 0 deform/create the loop defects in a way that the loop length never decreases. Starting from the topological sec- tor µ, loop defects can be created and grow larger, but this proce","work_id":"0797ce6d-6943-4613-a248-47973814b77f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"Wen, International Journal of Modern Physics B 4, 239 (1990)","work_id":"e314a2f9-395f-4b61-8e73-f3859e614bce","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"X.-G. Wen and Q. Niu, Physical Review B 41, 9377 (1990)","work_id":"dbf45aed-c949-4911-9bad-5aa1e5ffdb68","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"A. Kitaev and J. Preskill, Physical review letters 96, 110404 (2006)","work_id":"0a11371e-1e98-404e-a015-f789e4e57c0a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"M. Levin and X.-G. Wen, Physical review letters 96, 110405 (2006)","work_id":"172b1cbb-2f30-456e-83f7-45f37ad1b168","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":44,"snapshot_sha256":"9191544c409ab00a2c2c1d6d29722a0dee8c8315acf8f7ed2b438dcd0dbb1b5d","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"da13628e0fc5afa442b5b3cea22fab65bd1e63b6ee5d5d35fe45083eb3969474"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}