triqs.operators.util.U_matrix.U_matrix_kanamori

triqs.operators.util.U_matrix.U_matrix_kanamori(n_orb, U_int, J_hund, Up_int=None, full_Uijkl=False, Jc_hund=None)

Calculate the Kanamori interaction matrix (or full four-index tensor).

The two-index matrix for parallel spins is

\[U_{m m'}^{\sigma \sigma} \equiv U_{m m' m m'} - J_{m m'}\]

with

\[J_{m m'} \equiv U_{m m' m' m},\]

and the two-index matrix for anti-parallel spins is

\[U_{m m'}^{\sigma \bar{\sigma}} \equiv U_{m m' m m'}.\]

If full_Uijkl=True, the full four-index tensor is returned instead:

\[\begin{split}U_{m m m m} = U, \\ U_{m m' m m'} = U', \\ U_{m m' m' m} = J, \\ U_{m m m' m'} = J_C,\end{split}\]

with \(m \neq m'\).

Parameters:

n_orbint

Number of orbitals in the basis.

U_intfloat

Value of the screened Hubbard interaction.

J_hundfloat

Value of the Hund’s coupling.

Up_intfloat, optional

Value of the screened \(U'\) parameter. Defaults to U_int - 2 * J_hund (fully rotationally-invariant form).

full_Uijklbool, optional

If True, return the full four-index \(U_{ijkl}\) tensor instead of the two-index matrices. Default False.

Jc_hundfloat, optional

Used only when full_Uijkl=True. Defaults to J_hund.

Returns:

Unumpy.ndarray

Two-index interaction matrix for parallel spins (or the full four-index \(U_{ijkl}\) tensor when full_Uijkl=True).

Uprimenumpy.ndarray

Two-index interaction matrix for anti-parallel spins. Only returned when full_Uijkl=False.