The cumulant two-particle reduced density matrix as a measure of electron correlation and entanglement.
Several measures of electron correlation are compared based on two criteria: (i) the presence of a unique mapping between the reduced variables in the measure and the many-electron wave function and (ii) the linear scaling of the measure and its variables with system size. We propose the squared Frobenius norm of the cumulant part of the two-particle reduced density matrix (2-RDM) as a measure of electron correlation that satisfies these criteria. An advantage of this cumulant-based norm is its ability to measure the correlation from spin entanglement, which is not contained in the correlation energy. Alternative measures based on the 2-RDM, such as the von Neumann entropy, do not scale linearly with system size. Properties of the measures are demonstrated with Be, F(2), HF, N(2), and a hydrogen chain.
Juhász
Tamás
T
James Franck Institute, The University of Chicago, Chicago, IL 60637, USA.
Mazziotti
David A
DA
D000465:Algorithms; D001608:Beryllium / Q000737:chemistry; D004583:Electrons; D005461:Fluorine / Q000737:chemistry; D006858:Hydrofluoric Acid / Q000737:chemistry; D006859:Hydrogen / Q000737:chemistry; D009584:Nitrogen / Q000737:chemistry; D011789:Quantum Theory
D005461:Fluorine; D006859:Hydrogen; D009584:Nitrogen; D001608:Beryllium; D006858:Hydrofluoric Acid