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Algorithms

Here are some detailed explanations of the algorithms used in this package, however, it might still be too concise, please refer to the references for full discussion.

Moreover, a good starting point for the WF theory could be[RMP].

Wannierization

  • maximal localization for isolated bands, e.g. insulators
    • different from[MV97], optimize on unitary matrix manifolds (adaptation of [DLL19] to isolated bands)
  • disentanglement for entangled bands, e.g. metal
  • parallel transport gauge[GLS19]
    • you can further improve the spread by optimization w.r.t. a single rotation matrix[QMP21]
  • split valence and conduction WFs from a valence + conduction calculation[QMP21]
    • as a by-product, automated initial projection for valence or conduction WFs
    • for the initial projection of valence + conduction calculation, you can start with either conventional spdf projection, SCDM[DL18], or an automated projection and disentanglement from pseudopotential orbitals[QPM21]
    • different from SCDM, the valence+conduction manifold is chosen by the valence+conduction calculation, instead of SCDM μ and σ. Moreover, works in reciprocal space thus more memory-efficient
  • constrain WF center for max localization or disentanglement[QMP21]
    • similar to[WLPMM14], add an Lagrange multiplier term to spread functional, but optimize on matrix manifolds, and applying to both max localization and disentanglement (whereas in [WLPMM14] the center is constrained only during max localization)

Interpolation

Two algorithms:

  • Wigner-Seitz (WS) interpolation
  • Minimal-distance replica selection (MDRS) method

for band structure along a kpath or on a grid.

References