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pith:NW66XPHU

pith:2026:NW66XPHUBRZLHUROMUKAXAE2I2

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Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method

Gengzhi Yang, Hong-Zhou Ye

k-CIAH extends second-order CIAH optimization to k-point Pipek-Mezey Wannier functions while achieving O(N_k² n³) scaling.

arxiv:2602.12382 v2 · 2026-02-12 · physics.chem-ph · cond-mat.mtrl-sci

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Claims

C1strongest claim

By exploiting an efficient evaluation of the Hessian-vector product, k-CIAH achieves O(N_k^2 n^3) scaling in both CPU time and memory, matching that of previously reported first-order k-space approaches while improving upon the O(N_k^3 n^3) scaling of Γ-point CIAH... yields an overall computational efficiency approximately 2-3-fold higher than first-order k-space methods and orders of magnitude higher than Γ-point CIAH for localizing 1000-5000 orbitals. The quality of the resulting PMWFs is further validated by accurate electronic band structures obtained via PMWF-based Wannier interpolation.

C2weakest assumption

That the efficient Hessian-vector product evaluation in the k-CIAH extension maintains numerical stability and robust convergence for all tested systems (insulators, semiconductors, metals, surfaces) without hidden costs or post-hoc adjustments that affect the claimed scaling.

C3one line summary

k-CIAH enables efficient second-order optimization of Pipek-Mezey Wannier functions with O(N_k² n³) scaling, yielding 2-3x speedup over first-order k-space methods.

References

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[1] The special case in which this real-space unitary is constrained to be real-valued is discussed in sec- tion II G

[2] using the second-order co-iterative augmented Hes- sian (CIAH) algorithm. 43 CIAH is a modiﬁed trust-region Newton method46 that has been successfully applied to orbital localization in molecules 43,4

[3] (The Hessian diagonals are used to precondition the Davidson update

[4] We summarize the working equations be- low. We ﬁrst deﬁne two types of matrix elements of the atomic projection operators, (PTTT A,kkkkkk′)i j = 1 Nk ⟨φ kkki|ˆPTTT A|φ kkk′j⟩ = 1 Nk ∑ µ ∈ A O∗ TTT µ ,

[5] 35,38 In section IV, we compare the performance and computational efﬁciency of k-CIAH- and k-BFGS-based PMWF optimization

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Receipt and verification

First computed	2026-05-18T02:44:31.190282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6dbdebbcf40c72b3d22e65140b809a46a9b320935b425caba1e4b07f18ae9ebf

Aliases

arxiv: 2602.12382 · arxiv_version: 2602.12382v2 · doi: 10.48550/arxiv.2602.12382 · pith_short_12: NW66XPHUBRZL · pith_short_16: NW66XPHUBRZLHURO · pith_short_8: NW66XPHU

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/NW66XPHUBRZLHUROMUKAXAE2I2 \
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Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
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    "submitted_at": "2026-02-12T20:24:02Z",
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