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)[source]

Calculate the Kanamori two-index interaction matrix for parallel spins:

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

with:

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

and the two-index interaction matrix for anti-parallel spins:

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

If full_Uijkl=True is specified the full four index Uijkl 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_orb (integer) – Number of orbitals in basis.

  • U_int (float) – Value of the screened Hubbard interaction.

  • J_hund (float) – Value of the Hund’s coupling.

  • Up_int (float, optional) – Value of the screened U prime parameter defaults to U_int-2*J_hund if not given. (fully rotationally invariant form)

  • full_Uijkl (bool, optional) – retunr instead the full four-index Uijkl tensor default is False

  • Jc_hund (foat, optional) – only used if full_Uijkl=True, defaults to J_hund

Returns:

  • U (float numpy array) – The two-index interaction matrix for parallel spins or the four-index Uijkl tensor if full_Uijkl=True

  • Uprime (float numpy array) – The two-index interaction matrix for anti-parallel spins.