{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4EVPXFISUAH443Z5TGVLG4TTE2","short_pith_number":"pith:4EVPXFIS","schema_version":"1.0","canonical_sha256":"e12afb9512a00fce6f3d99aab3727326ae6a7c67c35db166b64ae45c1d50838a","source":{"kind":"arxiv","id":"2403.17069","version":2},"attestation_state":"computed","paper":{"title":"Tensor network formulation of symmetry protected topological phases in mixed states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Hanyu Xue, Jong Yeon Lee, Yimu Bao","submitted_at":"2024-03-25T18:04:29Z","abstract_excerpt":"We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which describe a broad class of short-range correlated mixed states, including the locally decohered SPT states. We map strong injective MPDO to a pure state in the doubled Hilbert space and define the SPT phases according to the cohomology class of the symmetry group in the doubled state. Although the doubled state exhibits an enlarged symmetry, the possible SPT"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2403.17069","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-25T18:04:29Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"1ddee472941720cab17d4c565cf569779c2a7b87e1298a8997ec64fbff72bb5a","abstract_canon_sha256":"b0d4d3fd95af366a28ea09bf42cd9becbb2b0847d8b77f1068d5d383eec564e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:19:43.758355Z","signature_b64":"DOyADJZvM6n63Yku2unF8G65T+f4HbJWCjonas9/wfkNgLrIbjh2M/trqTzLRW35yRPO+iB9fh0qU12lw+0yCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e12afb9512a00fce6f3d99aab3727326ae6a7c67c35db166b64ae45c1d50838a","last_reissued_at":"2026-07-05T08:19:43.757891Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:19:43.757891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor network formulation of symmetry protected topological phases in mixed states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Hanyu Xue, Jong Yeon Lee, Yimu Bao","submitted_at":"2024-03-25T18:04:29Z","abstract_excerpt":"We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which describe a broad class of short-range correlated mixed states, including the locally decohered SPT states. We map strong injective MPDO to a pure state in the doubled Hilbert space and define the SPT phases according to the cohomology class of the symmetry group in the doubled state. Although the doubled state exhibits an enlarged symmetry, the possible SPT"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17069","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.17069/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2403.17069","created_at":"2026-07-05T08:19:43.757958+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.17069v2","created_at":"2026-07-05T08:19:43.757958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17069","created_at":"2026-07-05T08:19:43.757958+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EVPXFISUAH4","created_at":"2026-07-05T08:19:43.757958+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EVPXFISUAH443Z5","created_at":"2026-07-05T08:19:43.757958+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EVPXFIS","created_at":"2026-07-05T08:19:43.757958+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.02555","citing_title":"Strong-to-Weak Spontaneous Symmetry Breaking","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2605.27193","citing_title":"Algebras of order parameters in one-dimensional spin systems","ref_index":139,"is_internal_anchor":false},{"citing_arxiv_id":"2605.28925","citing_title":"A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2406.19381","citing_title":"Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak","ref_index":46,"is_internal_anchor":false},{"citing_arxiv_id":"2509.24179","citing_title":"Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2602.10831","citing_title":"Mixed-State Topology in Non-Hermitian Systems","ref_index":68,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2","json":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2.json","graph_json":"https://pith.science/api/pith-number/4EVPXFISUAH443Z5TGVLG4TTE2/graph.json","events_json":"https://pith.science/api/pith-number/4EVPXFISUAH443Z5TGVLG4TTE2/events.json","paper":"https://pith.science/paper/4EVPXFIS"},"agent_actions":{"view_html":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2","download_json":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2.json","view_paper":"https://pith.science/paper/4EVPXFIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.17069&json=true","fetch_graph":"https://pith.science/api/pith-number/4EVPXFISUAH443Z5TGVLG4TTE2/graph.json","fetch_events":"https://pith.science/api/pith-number/4EVPXFISUAH443Z5TGVLG4TTE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2/action/storage_attestation","attest_author":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2/action/author_attestation","sign_citation":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2/action/citation_signature","submit_replication":"https://pith.science/pith/4EVPXFISUAH443Z5TGVLG4TTE2/action/replication_record"}},"created_at":"2026-07-05T08:19:43.757958+00:00","updated_at":"2026-07-05T08:19:43.757958+00:00"}