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-T_c superconductors, but focuses on the formation of local singlets.