{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XC2TXH7IBKUE4KCMOS4H4NCX6C","short_pith_number":"pith:XC2TXH7I","schema_version":"1.0","canonical_sha256":"b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743","source":{"kind":"arxiv","id":"2605.14414","version":1},"attestation_state":"computed","paper":{"title":"Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Katsunori Wakabayashi, Yuji Hamai","submitted_at":"2026-05-14T05:58:36Z","abstract_excerpt":"Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that unifies gauge smoothing and the eigenvalue problem of the projected position operator into a single deterministic framework. We demonstrate that discrete adiabatic transport across band degeneracies emerges naturally as an integral part of the solution procedure for the position eigenvectors. In this transport-aligned gauge, the Bloch overlaps exhibit an approxim"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-05-14T05:58:36Z","cross_cats_sorted":[],"title_canon_sha256":"c2971728da4ee9e5c79cf1f22cdd2df4ba4399dee49d1a2a88e6c858ac702197","abstract_canon_sha256":"310702de3bdff596954ac68ea9d69a8bd191172456d46fa68f7e14dd934a3ca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:07.328274Z","signature_b64":"JHvF39WG1/pS/M4/HBD5SfTouST8lv8uZFhQxILqgAWxDMeBm7EVZiy7wlbgVATmRRkW2hzCdx90UVjB46xBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743","last_reissued_at":"2026-05-17T23:39:07.327628Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:07.327628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Katsunori Wakabayashi, Yuji Hamai","submitted_at":"2026-05-14T05:58:36Z","abstract_excerpt":"Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that unifies gauge smoothing and the eigenvalue problem of the projected position operator into a single deterministic framework. We demonstrate that discrete adiabatic transport across band degeneracies emerges naturally as an integral part of the solution procedure for the position eigenvectors. In this transport-aligned gauge, the Bloch overlaps exhibit an approxim"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In this transport-aligned gauge, the Bloch overlaps exhibit an approximately linear phase dependence, allowing the Wannier centers to be extracted via deterministic fixed-point iterations and self-consistent updates rather than spread-functional minimization.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that discrete adiabatic transport across band degeneracies emerges naturally and produces approximately linear phase dependence in the Bloch overlaps for general systems, without post-hoc adjustments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A non-variational algorithm constructs maximally localized Wannier functions by treating discrete adiabatic transport across band degeneracies as part of solving the projected position operator eigenvalues, yielding linear phase overlaps and fixed-point extraction of centers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6ae1270ace259bdb611939fe745cc9ccc63a78d9e733665f7f5d36d777a33dca"},"source":{"id":"2605.14414","kind":"arxiv","version":1},"verdict":{"id":"7cd1b6c9-a0ba-45df-b266-9fd69bea09ef","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:03:40.902248Z","strongest_claim":"In this transport-aligned gauge, the Bloch overlaps exhibit an approximately linear phase dependence, allowing the Wannier centers to be extracted via deterministic fixed-point iterations and self-consistent updates rather than spread-functional minimization.","one_line_summary":"A non-variational algorithm constructs maximally localized Wannier functions by treating discrete adiabatic transport across band degeneracies as part of solving the projected position operator eigenvalues, yielding linear phase overlaps and fixed-point extraction of centers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that discrete adiabatic transport across band degeneracies emerges naturally and produces approximately linear phase dependence in the Bloch overlaps for general systems, without post-hoc adjustments.","pith_extraction_headline":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional."},"references":{"count":84,"sample":[{"doi":"","year":null,"title":"(33), (55) and (57), we have a WF with a candidate Wannier center r, |WM (r)⟩ = L− d/2 ∑ k e− ir·keik·( ˆx− M )|uk⟩, r ∈ [0,1)d","work_id":"382343cd-df90-4e1b-b6f5-61b366b199df","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The multidimensional formulation is given in Appendix D 4","work_id":"b0f6c243-4a3a-4b73-a329-6b091a06d80b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Matrix elements of ˆx In 1D cases, the real-space evaluation of the projected- position matrix elements Xs1s2 is explicitly calculated as fol- 10 FIG. 4. (Color online) Phases of the inner products of","work_id":"80c86021-84a2-421f-b74f-14161a3a379d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The spa- tial and k-space resolutions are N = 40 and L = 200, respec- tively","work_id":"7990b4b5-0ccc-47c7-8e57-86cb466a9d90","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The potential energy employed is of Kr¨ onig-Penney type, V (x) = ∑ V0 δ (x− n)","work_id":"3d0e2278-210f-4946-a246-60ea2b3f7092","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":84,"snapshot_sha256":"7e761c1a6e62c25100d7fe1a324b44e558bc67f49c0839793ffbeb2fc4ea0d68","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"330a73bc545273b59d2dab411db2527c270cbd93658c463248d36274cbf5a6c3"},"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":"2605.14414","created_at":"2026-05-17T23:39:07.327744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14414v1","created_at":"2026-05-17T23:39:07.327744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14414","created_at":"2026-05-17T23:39:07.327744+00:00"},{"alias_kind":"pith_short_12","alias_value":"XC2TXH7IBKUE","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"XC2TXH7IBKUE4KCM","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"XC2TXH7I","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C","json":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C.json","graph_json":"https://pith.science/api/pith-number/XC2TXH7IBKUE4KCMOS4H4NCX6C/graph.json","events_json":"https://pith.science/api/pith-number/XC2TXH7IBKUE4KCMOS4H4NCX6C/events.json","paper":"https://pith.science/paper/XC2TXH7I"},"agent_actions":{"view_html":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C","download_json":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C.json","view_paper":"https://pith.science/paper/XC2TXH7I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14414&json=true","fetch_graph":"https://pith.science/api/pith-number/XC2TXH7IBKUE4KCMOS4H4NCX6C/graph.json","fetch_events":"https://pith.science/api/pith-number/XC2TXH7IBKUE4KCMOS4H4NCX6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C/action/storage_attestation","attest_author":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C/action/author_attestation","sign_citation":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C/action/citation_signature","submit_replication":"https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C/action/replication_record"}},"created_at":"2026-05-17T23:39:07.327744+00:00","updated_at":"2026-05-17T23:39:07.327744+00:00"}