Entanglement Between Orbitals

Entanglement is one of the most fascinating concepts of modern physics. In striking contrast to its abstract and mathematical foundation, its practical side is remarkably underdeveloped: Even for the simplest scenario of just two orbitals or sites (“Hubbard dimer”) no faithful measure for generic mixed quantum states is known. By exploiting the spin symmetries of realistic electronic systems and implementing the fundamental superselection rule we succeed in deriving a compact formula for the relative entropy of entanglement between any two electronic orbitals. As a proof of concept, its first application already reveals a couple of striking insights: (i) The orbital correlation in molecular systems is mainly classical, rasing questions about the significance of entanglement for chemical bonding, (ii) the entanglement between most sites in the Hubbard model vanishes entirely, (iii) a local Fermi level-like structure can be restored within DMRG for off-lattice based on the division of correlation into its classical and quantum parts.