In the Jahn-Teller-Hubbard molecule, conventional quadrupoles vanish but composite two-body electron-phonon quadrupoles emerge that are selection-rule decoupled from them, and the ground-state entanglement involves phonon angular momenta L_ph=2,3 superposed with electron L=1,2 states.
The use of reduced matrix elements, however, allows one to factor out the angular- momentum coupling and thereby access quantities spe- cific to the electron or phonon sectors
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Spherical-tensor description of the Jahn--Teller--Hubbard molecule and local electron--phonon entanglement
In the Jahn-Teller-Hubbard molecule, conventional quadrupoles vanish but composite two-body electron-phonon quadrupoles emerge that are selection-rule decoupled from them, and the ground-state entanglement involves phonon angular momenta L_ph=2,3 superposed with electron L=1,2 states.