Principle of valence bond amplitude maximization in cuprates: Superconductivity and spin and charge ordering

The simple microscopic principle of valence-bond (nearest-neighbor singlet) amplitude maximization (VBAM) is shown to be present in undoped and optimally doped cuprates and unify the very different orderings such as antiferromagnetism in the Mott insulator and the robust superconductivity accompanied by an enhanced charge and stripe correlations in the optimally doped cuprates. VBAM is nearly synonymous with the energy minimization principle. It is implicit in the resonating valence bond (RVB) theory and thereby makes the predictions of RVB mean field theory of superconductivity qualitatively correct.