Figure 1

The region with binding of holes in the $J-J_{\mathrm{AF}}$ plane, for different cluster shapes with OBC. The solid line corresponds to ${\Delta }_B=-0.1$.Reuse & Permissions

Figure 2

Pair-binding energies ${\Delta }_B$ vs $1/L$ for a chain (a), a two-leg ladder (b), and square clusters (c). (d) ${\Delta }_B$ vs $1/m$ for the cluster $6\times 6$, at couplings indicated.Reuse & Permissions

Figure 3

(a) $-{\Delta }_B$ vs $J$ for the clusters $1\times 10$, $2\times 6$, and $3\times 3$ with OBC. Inset: The nearest-neighbor spin-spin ($S(1)$) and hole-hole ($N(1)$) correlations, measured in the center of the $2\times 6$ cluster with 2-holes and $J_{\mathrm{AF}}=0.75$, as function of $J$. (b) The pair-pair correlation function $C(l)$ vs $l$ for a system size $2\times 32$ and $J_{\mathrm{AF}}=0.75$ with 8 holes, for some values of $J$. The straight lines are data fits with the powers indicated by the arrows. (c) $P$ vs $J$ for the cluster $2\times 32$ with 2 and 8 holes and some values of $J_{\mathrm{AF}}$. (d) The spin structure factor $S(\pi ,\pi )$ vs $J_{\mathrm{AF}}$ for the clusters $1\times 20$, $2\times 10$ and $4\times 4$, at $J=2$ and half-filling.Reuse & Permissions

Figure 4

Schematic phase diagram of the HKLM close to half-filling. The solid line defines the region where $d$-wave SC should exist based on our numerical calculations. The yellow region is the long-range AF phase. The dashed line describes a trajectory with increasing pressure that is compatible with HF experiments (see text).Reuse & Permissions