Strongly Correlated Electrons

Michael Seidl

Electrons can have a given smooth density distribution $\ensuremath{\rho}(r),$ even if their Coulomb interaction is scaled to infinity. This strong-interaction limit of density-functional theory provides essential information on the correlation energy of real electron systems. The simple concept of strictly correlated electrons (SCE) is analyzed here as a model for that limit. SCE is solved exactly for any one-dimensional (1D) N-electron density and, in particular, for any 3D spherical two-electron system, such as the helium atom. Both the SCE interaction energy and the SCE external potential, which are obtained here as density functionals, obey all the relations known for the corresponding quantities in the unknown true strong-interaction limit. At large but finite interaction, the electrons are still strongly correlated, performing zero-point oscillations about the SCE limit.

S. V. Kravchenko

Dimitrios Galanakis

In this thesis we are going to study the properties of strongly correlated electron systems (SCES) using analytical, phenomenological and computational methods. In the introductory chapter we will discuss generally the problem of strongly correlated electron systems and the methods that are used to analyse their behavior. In chapter 2, we discuss the derivation of low energy effective theories by using perturbation theory. In chapter 3, we point out potential problems with perturbative techniques used to construct low energy theories for SCES. In chapter 4, we introduce an important class of materials, namely the cobaltates NaxCoO2 and we discuss the experiments that establish their strongly correlated electron nature. The cobaltates exhibit a novel insulating state at x = 0.5 which corresponds to a 3/4 filled band. This state is analyzed phenomenologically in chapter 5. In chapter 6, we introduce a non perturbative technique appropriate for strongly correlated electron systems, the Dynamical Mean Field Theory (DMFT) and its cluster extension. The results of the application of cluster DMFT on the cobaltates are presented in chapter 7.

Takashi Yanagisawa, Masanori Miyazaki, Yamaji K.

We investigate the electronic properties of the ground state of strongly correlated electron systems. We use an optimization variational Monte Carlo method for the two-dimensional Hubbard model and the three-band d-p model. The many-body wavefunction is improved and optimized by introducing variational parameters that control the correlation between electrons. The on-site repulsive Coulomb interaction U induces strong antiferromagnetic (AF) correlation. There is a crossover from weakly to strongly correlated regions as U increases. We show an idea that high-temperature superconductivity occurs as a result of this crossover in the strongly correlated region where U is greater than the bandwidth.

Victor J. Emery