pythtb.Wannier.set_tilde_states#

Wannier.set_tilde_states(states, is_cell_periodic=True, is_spin_axis_flat=False)[source]#

Set the Bloch-like states for the Wannier functions.

These states are Fourier transformed to form the Wannier functions. They are related to the original energy eigenstates via the (semi-) unitary transformation

\[|\tilde{\psi}_{n\mathbf{k}} \rangle = \sum_{m=1}^{N} U_{mn}^{(\mathbf{k})} |\psi_{m\mathbf{k}} \rangle\]
Parameters:
statesnp.ndarray

The states to set as Bloch-like states. Must have the shape (nk1, ..., nstates, n_orbs[, n_spins]).

is_cell_periodicbool, optional

Whether to treat states as cell-periodic parts \(u_{n\mathbf{k}}\).

is_spin_axis_flatbool, optional

Whether the spin dimension is flattened into the orbital dimension. If True, states must have shape (nk1, ..., nstates, n_orbs*n_spins). If False, states must have shape (nk1, ..., nstates, n_orbs, n_spins). Defaults to False.

Raises:
ValueError

If the input states are not a numpy array or have an invalid shape.

Notes

  • If is_cell_periodic is True, the states are treated as cell-periodic parts of Bloch functions \(u_{n\mathbf{k}}\), otherwise as full Bloch functions \(\psi_{n\mathbf{k}}\).

  • If is_spin_axis_flat is False and wavefunctions have spin, states are reshaped to flatten the spin dimension into the orbital dimension.

  • The Wannier functions, spreads, and centers are computed upon setting the Bloch-like states.