Fig. 2.

(A) Exact diagonalization (ED) energies of the lowest-lying states in three charge sectors (indicated in legend) for both the $4\times 4$ site (triangular markers) and $6\times 2$ site systems (circles). (B) Plot of $E_{2e}/2-E_{1e}$ vs. U, whose negative value indicates electron pairing. (C) ED energy spectrum on the $6\times 2$ site torus at $U/t=5$. The energies are arranged by total spin $S_z$ and electric charge Q (indicated in legend); they organize into multiplets of the spin and pseudospin SU(2) symmetries. (D) Overlap of the spin-singlet pairing operator $c_{\mathit{r}}^{\mathsf{T}}(i{s}_y)c_{\mathcal{O}}$ between the half-filled ground state and two-electron excitation for all sites $\mathit{r}$ on a $4\times 4$ site torus at $U/t=6$, with origin indicated by $\mathcal{O}$. Its magnitude and phase are specified by marker area and color, respectively.