triqs.operators.util.observables.L2_op

triqs.operators.util.observables.L2_op(spin_names, orb_names, off_diag=None, map_operator_structure=None, basis='spherical', T=None)[source]

Create the square of the orbital momentum operator.

\[\hat L^2 = \hat L_x^2 + \hat L_y^2 + \hat L_z^2.\]
Parameters:

  • spin_names (list of strings) – Names of the spins, e.g. [‘up’,’down’].

  • orb_names (list of strings or int) – Names of the orbitals, e.g. [0,1,2] or [‘t2g’,’eg’].

  • off_diag (boolean) – Do we have (orbital) off-diagonal elements? If yes, the operators and blocks are denoted by (‘spin’, ‘orbital’), otherwise by (‘spin_orbital’,0).

  • map_operator_structure (dict) – Mapping of names of GF blocks names from one convention to another, e.g. {(‘up’, 0): (‘up_0’, 0), (‘down’, 0): (‘down_0’,0)}. If provided, the operators and blocks are denoted by the mapping of ('spin', 'orbital').

  • basis (string, optional) –

    The basis in which the interaction matrix should be computed. Takes the values

    • ’spherical’: spherical harmonics,

    • ’cubic’: cubic harmonics (valid only for the integer orbital momenta, i.e. for odd sizes of orb_names),

    • ’other’: other basis type as given by the transformation matrix T.

  • T (real/complex numpy array, optional) – Transformation matrix for basis change. Must be provided if basis=’other’.

Returns:

L2 – The square of the orbital momentum operator.

Return type:

Operator