ffsim.contract.diag_coulomb_linop

ffsim.contract.diag_coulomb_linop(mat, norb, nelec, *, orbital_rotation=None, z_representation=False)

Convert a (rotated) diagonal Coulomb matrix to a linear operator.

A rotated diagonal Coulomb operator has the form

\[\begin{split}\mathcal{U} (\sum_{\substack{ij \\ \sigma \tau}} Z^{(\sigma \tau)}_{ij} n_{i\sigma} n_{j\tau} / 2) \mathcal{U}^\dagger\end{split}\]

where \(n_{i\sigma}\) denotes the number operator on orbital \(i\) with spin \(\sigma\), \(Z^{(\sigma \tau)}\) is a real-valued matrix, and \(\mathcal{U}\) is an optional orbital rotation.

Parameters:

• mat (ndarray | tuple[ndarray | None, ndarray | None, ndarray | None]) – The diagonal Coulomb matrix \(Z\). You can pass either a single Numpy array specifying the coefficients to use for all spin interactions, or you can pass a tuple of three Numpy arrays specifying independent coefficients for alpha-alpha, alpha-beta, and beta-beta interactions (in that order). If passing a tuple, you can set a tuple element to None to indicate the absence of interactions of that type.

• norb (int) – The number of spatial orbitals.

• nelec (tuple[int, int]) – The number of alpha and beta electrons.

• orbital_rotation (ndarray | tuple[ndarray | None, ndarray | None] | None) – The optional orbital rotation. You can pass either a single Numpy array specifying the orbital rotation to apply to both spin sectors, or you can pass a pair of Numpy arrays specifying independent orbital rotations for spin alpha and spin beta. If passing a pair, you can use None for one of the values in the pair to indicate that no operation should be applied to that spin sector.

• z_representation (bool) – Whether the input matrices are in the “Z” representation.

Return type:

LinearOperator

Returns:

A LinearOperator that implements the action of the diagonal Coulomb operator.