Modified Perturbation Theory for Strongly Correlated Electron Systems

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.

H. Keiter, Srećko Kilić

Tran Minh-Tien

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The dynamical cluster approximation and the cellular dynamical mean field theory are related each other through the canonical transformation. A cluster perturbation theory with periodic boundary conditions is developed. It is found that the periodic cluster perturbation theory converges rapidly with corrections $\mathcal{O}(1/L_c^2)$, where $L_c$ is the linear size of the clusters, whereas the ordinary cluster perturbation theory converges with corrections $\mathcal{O}(1/L_c)$.

H. Keiter, Srećko Kilić, Sven Oberbach

Markus Aichhorn, Maria Daghofer, Hans Gerd Evertz +1 more

We present a modified finite-temperature Lanczos method for the evaluation of dynamical and static quantities of strongly correlated electron systems that complements the finite-temperature method introduced by Jakli\ifmmode \check{c}\else \v{c}\fi{} and Prelov\ifmmode \check{s}\else \v{s}\fi{}ek for low temperatures. Together they allow accurate calculations at any temperature with moderate effort. As an example we calculate the static spin-correlation function and the regular part of the optical conductivity ${\ensuremath{\sigma}}^{\mathrm{reg}}(\ensuremath{\omega})$ of the one-dimensional Hubbard model at half filling and show in detail the connection between the ground-state and finite-temperature method. By using cluster perturbation theory, the finite-temperature spectral function is extended to the infinite system, clearly exhibiting the effects of spin-charge separation.

Karan Aryanpour