Download file (12.6 MB)
Download as zip (12.4 MB)

Collection

Citation

Description:

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 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. Benchmark calculations for one- and two-dimensional systems yield spreads and orbital shapes in good agreement with standard minimization schemes. Furthermore, this analytical approach transparently isolates the physical origin of the mesh-dependent spread scaling ( being the boundary seam resolution) observed in graphene, demonstrating that it is an intrinsic geometric manifestation of non-commuting projected position operators forcing finite gauge defects to accumulate along a one-dimensional boundary seam.

Rights:

• In Copyright
  

  ©2026 The Physical Society of Japan

Keyword: Wannier function, maximally localized Wannier function, density functional theory, adiabatic transport theory, Berry phase, Zak phase, Wilson loop

Date published: 2026-07-15

Publisher: National Institute for Materials Science

Journal:

• Journal of the Physical Society of Japan (ISSN: 13474073) vol. 95 issue. 7 074704

Funding:

• Japan Society for the Promotion of Science JP25K01609
• Japan Society for the Promotion of Science JP22H05473
• Japan Society for the Promotion of Science JP21H01019
• Japan Science and Technology Corporation JPMJCR19T1
• Sumitomo Foundation 2401203

Manuscript type: Author's version (Accepted manuscript)

MDR DOI: https://doi.org/10.48505/nims.6338

First published URL: https://doi.org/10.7566/jpsj.95.074704

Related item:

Other identifier(s):

Contact agent:

Updated at: 2026-06-16 11:13:40 +0900

Published on MDR: 2026-06-16 12:26:17 +0900