Short-range spin correlations and induced local spin-singlet amplitude in the Hubbard model

In this paper, from the microscopic Hubbard Hamiltonian we extract the local spin-singlet amplitude due to short-range spin correlations, and quantify its strength near half-filling. As a first application of the present approach, we study a problem of the energy dispersion and its d-wave modulation in the insulating cuprates, Sr${}_2$CuO${}_2$Cl${}_2$ and Ca${}_2$CuO${}_2$Cl${}_2$. Without any adjustable parameters, most puzzling issues are naturally and quantitatively explained within the present approach.