**Universität Regensburg**

Institut für Theoretische Physik

Dr. Thomas Maier

**Abstract zur Arbeit**:

*Nonlocal Dynamical Correlations in Strongly Interacting
Fermion Systems*

Diss., Universität Regensburg

Logos Verlag Berlin 2001

ISBN: 3-89722-599-9

Autor: Thomas Maier

Betreuer: PD Dr. Thomas Pruschke

Abgabe: 14. Dezember 2000

Kolloquium: 8. Februar 2001

In this thesis a cluster approach for the thermodynamic limit to study intersite correlations in strongly interacting Fermionic systems is presented. The Dynamical Cluster Approximation (DCA) is a systematic extension of the Dynamical Mean Field approach, which treats short-ranged correlations exactly while approximating the effect of the longer-ranged physics. The DCA may be derived by coarse-graining the reciprocal space, which maps the problem onto a periodic cluster model embedded in a self-consistently determined host. A massive reduction in the complexity of the problem is thus obtained. A generalization of the Non Crossing Approximation (NCA) to solve the effective cluster problem is developed. The NCA diagonalizes the cluster problem and then performs a resummation of certain classes of diagrams to all orders in a perturbational expansion in the coupling to the host. By further extending this combined DCA/NCA approach to handle symmetry broken states, properties of possible antiferromagnetic and superconducting phases can be studied down to very low temperatures ( 10K).

The DCA/NCA approach is used to investigate the single-particle properties of the two-dimensional (2D) Hubbard model and some related aspects of the 2D tJ-model; these models are believed to capture the main features of the low-energy electronic behavior of the -layers in high-temperature superconductors. The fundamental features of their experimental phase diagram can be described with the DCA/NCA approach: At half-filling a transition to an antiferromagnetic phase is observed. Nonlocal correlations are found to suppress ordering.

Upon doping, the system exhibits a crossover from non-Fermi liquid to Fermi liquid behavior. At weak doping ( ), a pseudogap is found to develop in the low-energy density of states with decreasing temperature accompanied by a dramatic suppression of spin excitations. Upon further doping ( ), the pseudogap diminishes and Fermi liquid behavior appears to be recovered.

As a main result, an instability to the superconducting state is found even in the strong coupling regime of the model with a maximum critical temperature occurring at 20% doping. The corresponding order parameter has -wave symmetry consistent with experiments.