Fig. 3.

(A) Illustration of the infinite-length $\text{XC}4$ cylinder with circumference $L_y=2\sqrt{3}a$, where a is the lattice spacing. The “segment” DMRG method consists of optimizing a finite number of tensors (describing $N_r$ cylinder rings) sandwiched between two semi-infinite MPS environments derived from a reference (half-filled) ground state with bond dimension ${\chi }_{\text{undoped}}$. (B) Electron pairing energy $E_{2e}/2-E_{1e}$ vs. maximum magnitude Λ of discarded singular values in the finite segment, with legend indicating ${\chi }_{\text{undoped}}$. (C) Upper panel: energies of excitations with charges $(Q,S_z)$ (indicated in legend) vs. Hubbard U, with fixed ${\chi }_{\text{undoped}}=1,024$ and $\mathrm{\Lambda }={10}^{-5}$. The legend indicates $N_r$ (increasing light to dark). Lower panel: electron pairing energy vs. U. (D) Magnitude of the pair wavefunction at both $U/t=4$ and $U/t=10$, computed from respective iDMRG ground states with ${\chi }_{\text{undoped}}=1,024$ and segment excitations with $N_r=120$. The two dotted lines are related under the cylinder identification; outside points are periodic images. (E) Correlation lengths of the half-filled YC6 ground state in the $1e$ (Left panel) and $2e$ (Right) sectors, in units of cylinder rings, as a function of bond dimension (increasing light to dark) and U.