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Locally gauge invariant theory of large U_d high-Tc cuprates

The large U_d theory, based on the Emery three band model extended with the Ox-Oy hopping t_pp, is constructed for the metallic state of high-Tc cuprates, using the mapping on the slave fermion theory. The time-dependent diagrammatic theory in terms of the Cu-O hopping t_pd starts from the locally gauge invariant state with vanishing occupation of the Cu state and builds a finite n_d in higher orders. This theory is locally gauge invariant asymptotically, but replaces the d-p anticommutation between the Cu and O sites by the commutation and is antisymmetrized a posteriori. Rather than t_pd, the small parameter of the theory is n_d less or equal to 1/2. The leading many body effect is band narrowing, different from the mean-field one. It is accompanied by the d10-d9 intracell charge transfer disorder, which breaks the Luttinger sum rule for the conduction band. The corresponding damping of the single particle propagation is situated well below the Fermi level. The effective local repulsions between the hybridized pdp propagators show up beyond the third order. The a posteriori antisymmetrization removes the triplet repulsion between the pdp particles but keeps the singlet repulsion which favors incommensurate SDW correlations at low energy. Such repulsion is the metallic counterpart of the superexchange J_pd between the dpd propagators. Resonant valence bonds thus appear as perturbative corrections. The resulting theory is shown to compare favorably with numerous experiments, emphasizing the physical importance of the oxygen degrees of freedom.