We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions $V^{S}$ that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions $H^{SB}$ that lead to decoherence influence the correlation energy. The effects only decouple when $[V^{S},H^{SB}]=[H^{S},H^{SB}]=0$ , where $H^{S}$ is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions $V^{S}$ that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions $H^{SB}$ that lead to decoherence influence the correlation energy. The effects only decouple when $[V^{S},H^{SB}]=[H^{S},H^{SB}]=0$, where $H^{S}$ is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.

Jun 3, 20151 citation

Strong Correlation in Molecular Periodic Systems from a Variational Reduced Density Matrix Theory

Simon Ewing, David A. Mazziotti

Molecular periodic systems have the challenge of not only representing an infinite, albeit periodically repeating, molecule but also treating the strong electron correlation that emerges in such systems. Many post-Hartree-Fock methods that are efficient in moderately correlated molecules often fail to describe strongly correlated electrons and their properties in periodic systems. Here we develop and apply an electronic structure approach to periodic systems based on the variational calculation of the two-electron reduced density matrix (2-RDM). The variational 2-RDM method calculates a lower bound to the ground-state energy of a molecular periodic system without computation or storage of its many-electron wave function. The 2-RDM is constrained by $N$ -representability conditions that are necessary for it to represent at least one $N$ -electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.Molecular periodic systems have the challenge of not only representing an infinite, albeit periodically repeating, molecule but also treating the strong electron correlation that emerges in such systems. Many post-Hartree-Fock methods that are efficient in moderately correlated molecules often fail to describe strongly correlated electrons and their properties in periodic systems. Here we develop and apply an electronic structure approach to periodic systems based on the variational calculation of the two-electron reduced density matrix (2-RDM). The variational 2-RDM method calculates a lower bound to the ground-state energy of a molecular periodic system without computation or storage of its many-electron wave function. The 2-RDM is constrained by $N$-representability conditions that are necessary for it to represent at least one $N$-electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.

Aug 6, 20202 citations

Electron Correlation in the Solid State

N. H. March

IMPERIAL COLLEGE PRESS eBooksDec 1, 199929 citations

V^{S}

that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions

H^{SB}

that lead to decoherence influence the correlation energy. The effects only decouple when

[V^{S},H^{SB}]=[H^{S},H^{SB}]=0

, where

H^{S}

is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.

N

-representability conditions that are necessary for it to represent at least one

N

-electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.