Pith Number

pith:XC2TXH7I

pith:2026:XC2TXH7IBKUE4KCMOS4H4NCX6C

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Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport

Katsunori Wakabayashi, Yuji Hamai

Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.

arxiv:2605.14414 v1 · 2026-05-14 · cond-mat.mtrl-sci

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

84 extracted · 84 resolved · 1 Pith anchors

[1] (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

[2] The multidimensional formulation is given in Appendix D 4

[3] 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

[4] The spa- tial and k-space resolutions are N = 40 and L = 200, respec- tively

[5] The potential energy employed is of Kr¨ onig-Penney type, V (x) = ∑ V0 δ (x− n)

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:07.327628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743

Aliases

arxiv: 2605.14414 · arxiv_version: 2605.14414v1 · doi: 10.48550/arxiv.2605.14414 · pith_short_12: XC2TXH7IBKUE · pith_short_16: XC2TXH7IBKUE4KCM · pith_short_8: XC2TXH7I

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XC2TXH7IBKUE4KCMOS4H4NCX6C \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "310702de3bdff596954ac68ea9d69a8bd191172456d46fa68f7e14dd934a3ca7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mtrl-sci",
    "submitted_at": "2026-05-14T05:58:36Z",
    "title_canon_sha256": "c2971728da4ee9e5c79cf1f22cdd2df4ba4399dee49d1a2a88e6c858ac702197"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}