This book contains lectures on strongly correlated electron systems presented by eminent physicists. These lectures are up-to-date summaries of relevant subjects in the field of condensed matter physics intended to train students. Contributions include: strongly correlated electron behaviors and heavy Fermions in anomalous rare-earth and actinide systems; strong correlations in low dimensional systems; functional renormalization group approach to correlated electron systems; and numerical approaches to coupled quantum systems.
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.