{"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"}