pythtb.Wannier

class Wannier(bloch_states)

Construct Wannier functions through the projection method.

This class implements projection, disentanglement [2], and maximal-localization [1] workflows using Bloch states represented in a finite tight-binding orbital basis. The high-level workflow is:

1. Single-shot SVD projection to trial functions (project()).

2. Optional disentanglement in an outer/frozen window (disentangle()).

3. Unitary gauge optimization for maximal localization (maxloc()).

Parameters:

bloch_statesWFArray

Bloch-like states to Wannierize. The mesh must be a torus in k-space (no endpoint duplication), and states must already be populated.

Notes

• Wannier performs a re-Wannierization relative to typical Wannier90 workflows:

  • Wannier90 commonly starts from first-principles Bloch states and projects onto trial orbitals, typically taking the form of localized atomic orbitals.

  • Wannier works directly with WFArray states and trial functions expressed in the same tight-binding orbital/spin basis.

• Wannier functions are obtained from Bloch-like states \(\tilde{\psi}_{n\mathbf{k}}\) via inverse FFT over k-axes:

  \[w_{n\mathbf{R}} = \frac{1}{\sqrt{N_k}} \sum_{\mathbf{k}} e^{i\mathbf{k}\cdot\mathbf{R}} \tilde{\psi}_{n\mathbf{k}}.\]

References

[1]

Marzari, N., & Vanderbilt, D. Phys. Rev. B 56, 12847 (1997).

[2]

Souza, I., Marzari, N., & Vanderbilt, D. Phys. Rev. B 65, 035109 (2001).

Methods

pythtb.Wannier.disentangle	Disentanglement of a subspace that minimizes gauge-independent spread.
pythtb.Wannier.get_centers	Return Wannier centers in Cartesian or fractional coordinates.
pythtb.Wannier.get_trial_wfs	Build normalized trial-wavefunction array from tuple specifications.
pythtb.Wannier.info	Print a formatted report of Wannier centers and spreads.
pythtb.Wannier.interp_bands	Wannier interpolate the band structure along a k-path.
pythtb.Wannier.maxloc	Unitary transformation to minimize the gauge-dependent spread.
pythtb.Wannier.min_spread	Run disentanglement + projection + maximal-localization workflow.
pythtb.Wannier.plot_centers	Plot the Wannier function centers in the supercell.
pythtb.Wannier.plot_decay	Plot the Wannier function density as a function of distance from center.
pythtb.Wannier.plot_density	Plot the Wannier function density on the lattice in 2D.
pythtb.Wannier.project	Initialize or update Bloch-like states by projection onto trial functions.
pythtb.Wannier.set_tilde_states	Set the Bloch-like states for the Wannier functions.
pythtb.Wannier.set_trial_wfs	Set trial wavefunctions for Wannierization.

Attributes

pythtb.Wannier.Amn	Overlap matrix between reference states and trial wavefunctions.
pythtb.Wannier.Omega_D	Diagonal gauge-dependent spread \(\Omega_{\mathrm{D}}\).
pythtb.Wannier.Omega_I	Gauge-invariant spread \(\Omega_I\).
pythtb.Wannier.Omega_OD	Off-diagonal gauge-dependent spread \(\Omega_{\mathrm{OD}}\).
pythtb.Wannier.bloch_states	Input Bloch states to be Wannierized.
pythtb.Wannier.centers	Wannier centers in Cartesian coordinates.
pythtb.Wannier.lattice	Lattice associated with this Wannier workflow.
pythtb.Wannier.mesh	Mesh associated with this Wannier workflow.
pythtb.Wannier.nks	Number of k points along each k-axis.
pythtb.Wannier.num_twfs	Number of trial wavefunctions.
pythtb.Wannier.spread	Quadratic spread \(\Omega_n\) for each Wannier function.
pythtb.Wannier.tilde_states	Bloch-like states \(\tilde{\psi}_{n\mathbf{k}}\).
pythtb.Wannier.trial_wfs	Trial wavefunctions used for projection.
pythtb.Wannier.wannier	Wannier functions in the supercell implied by the k-grid.