and consider the bonding wavefunction given by Eq. (1) at half filling. The assumptions about Eq. (10) are discussed in Appendix A. While there exists another state $ | \Psi _{BB} \rangle = c ^{\dagger} _{B \uparrow} c ^{\dagger} _{B \downarrow} |0 \rangle$, as mentioned in Appendix B, its contribution is small and we can include it just by performing an orbital transformation. For convenience, I introduce my model without considering $ | \Psi _{BB} \rangle$ in the main text, and include its contribution in Appendix B by using such a transformation to preserve the form of Eq. (1).

Because the bonding electrons in the covalent limit are described by the linear combination of the AF states $ c_{A \uparrow} ^{\dag} c_{B \downarrow} ^{\dag} | 0 \rangle$ and $ c_{B \uparrow} ^{\dag} c_{A \downarrow} ^{\dag} | 0 \rangle$, it is natural to try the extended AF density matrix $\rho _{ea}$ to construct the quasielectron orbitals of the one-bond system in Fig. 1 (a). In each AF state one electron is located at $ | A \rangle$ while the other one is located at $ |B \rangle$, so we shall take the matrices $\rho ^{(1)}$ and $\rho ^{(2)}$ in Eq. (8) 