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Plaquette Valence Bond Theory of High-Temperature Superconductivity

We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the t,t' Hubbard model. The crossing of ground state energies in the N=2,3,4 sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the d(x2-y2)-wave order parameter at the border between localized and itinerant electron behavior and gives a natural explanation for the pseudo-gap formation via soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence bond theory stressing a crucial role of singlets in the physics of high-Tc superconductors, but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.