Hole pairs in a spin liquid: Influence of electrostatic hole-hole repulsion

The stability of hole bound states in the $t-J$ model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2\times 30$ sites. For a nearest-neighbor (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J.\mathrm{}$ At $\sim 10\%$ hole doping the pairs break only for a NN repulsion as large as $V\sim 4J.$ Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper oxides is remarked.