Quantum-Monte-Carlo studies of superconductivity in strongly correlated systems

Quantum-Monte-Carlo (QMC) simulations are reviewed, which aim at a quantitative understanding of the multi-orbital 2-D Hubbard model, as it relates to the unusual properties of the normal state of the high-Tc cuprates and possibly to the microscopic nature of the superconducting pairing. In a first step, by comparing QMC results with experimental data on electronic and magnetic excitations, a unique parameter set is determined which clearly (also for dopings x ≠ 0) places the high-Tc cuprates in the strongly correlated regime. A new dynamical extension of the QMC technique reveals that the states near EF are related to the Zhang-Rice Cu - O singlet construction. They are found to have a band-like dispersion with also Fermi velocity and location in close accord with photoemission data. Whereas the imaginary part of the self-energy displays non-Fermi liquid behavior for smaller dopings (x ≅ 0.25), for larger dopings (x ≅ 0.5) the Fermi liquid picture is restored. Besides the normal state properties we also extract superconducting pair-field susceptibilities for various symmetry channels. As a particularly noteworthy result, we find the interaction vertex in the extended s-channel to show a maximum for x ∝ 0.2, closely resembling the experimental dependence of Tc on doping. (orig.)