triqs_modest.hamiltonians.U_matrix_in_spherical_basis

triqs_modest.hamiltonians.U_matrix_in_spherical_basis()

Dispatched C++ function(s).

[1] (l: int, U_int: float, J_hund: float)
  -> ndarray[float, 4]

Construct a four-index Coulomb tensor in the basis of spherical harmonics.

We typically construct the four-index Coulomb tensor in the basis of spherical harmonics,

\[U_{m_{1}m_{2}m_{3}m_{4}}^{\mathrm{spherical}} = \sum_{k=0}^{2l} F_{k} \alpha (l, k, m_{1}, m_{2}, m_{3}, m_{4}),\]

where \(F_{k}\) are radial Slater integrals and \(\alpha(l, k, m_{1}, m_{2}, m_{3}, m_{4})\) denote angular Racah-Wigner numbers for a spherically symmetric interaction tensor.

Parameters:

lint

Angular quantum number.

U_intfloat

Screened Hubbard interaction.

J_hundfloat

Hund’s coupling.

Returns:

ndarray[float, 4]

Coulomb tensor.