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Werner Hanke1, Markus Aichhorn1, Sascha Brehm1, Enrico Arrigoni2 and Michael Potthoff3 1 University of Würzburg, Institute for Theoretical Physics & Astrophysics, Theoretical Physics 1, Am Hubland, 97074 Würzburg, Germany. 2 Technical University of Graz, Institute for Theoretical Physics, Petersgasse 16, 8010 Graz, Austria. 3 University of Hamburg, 1st Institute for Theoretical Physics, Jungiusstr. 9, 20355 Hamburg, Germany We review results obtained via a recently proposed variational quantum-cluster approach (VCA) for the (T=0) single-particle (photoemission) and two-particle (spin- and charge) excitation spectra and for the phase diagram of the two-dimensional Hubbard model. The VCA, which presents a controlled route to translate the microscopic cluster information to the infinite-size lattice, reproduces the overall ground-state phase diagram of the high-temperature superconductors, both for electron- and hole-doping. The phase diagram includes salient features, such as the enhanced robustness of the antiferromagnetic (AF) state as a function of electron doping and the tendency toward phase separation into a mixed AF-superconducting (SC) phase at low doping and a pure SC phase at high (both electron- and hole-) doping. A similar variational cluster scheme is presented for extracting two-particle correlation functions. As a first application, we analyze the doping evolution of the spin-susceptibility and its characteristic low-energy excitations. Experimental features (e. g. resonant magnetic excitations in the SC state) are identified, which lend further credibility to a description by Hubbard-type models. Finally, the question of a "pairing glue" is studied both for the single- and 3-band Hubbard models. To this a measure for the frequency dependence of the pairing interaction is introduced. It allows for checking whether the interaction is instantaneous on the relative time scales of interest or corresponds to the traditional picture of a retarded interaction. |
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