pythtb.Wannier.Omega_I

property Wannier.Omega_I

Gauge-independent quadratic spread.

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 gauge-invariant part \(\Omega_I\) is independent of the choice of Wannier gauge. It is computed via

\[\Omega_I = \frac{1}{N_k} \sum_{\mathbf{k}, \mathbf{b}} w_b \left( N_{\rm bands} - \sum_{m,n} |M_{mn}^{(\mathbf{b})}(\mathbf{k})|^2 \right)\]