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.
(F7) Because this is a 1 × 1 overlap matrix, its singular value is simply σ s α (k) = |ms α (k)|
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Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport
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.