pythtb.Wannier.Omega_D

property Wannier.Omega_D

Diagonal gauge-dependent spread \(\Omega_{\mathrm{D}}\).

Part of the decomposition of the quadratic spread into gauge-invariant (\(\widetilde{\Omega}\)) and gauge-dependent (\(\widetilde{\Omega}\)) parts,

\[\Omega = \widetilde{\Omega} + \Omega_I = \Omega_{\rm OD} + \Omega_{\rm D} + \Omega_I\]

The diagonal part \(\Omega_{\rm D}\) is computed via

\[\Omega_{\rm D} = \frac{1}{N_k} \sum_{\mathbf{k}, \mathbf{b}} w_b \sum_n \left( -\operatorname{Im}\!\left[\ln M_{nn}^{(\mathbf{b})}(\mathbf{k})\right] - \mathbf{b}\cdot\mathbf{r}_n \right)^2\]

Returns:

float

Diagonal spread contribution.

Raises:

ValueError

If tilde states are not initialized.