Superconductivity in the Two-Dimensional $t$-$J$ Model at Low Hole Doping

By combining a generalized Lanczos scheme with the variational Monte Carlo method we can optimize the short- and long-range properties of the groundstate separately. This allows us to measure the long-range order of the groundstate of the $t$-$J$ model as a function of the coupling constant $J/t$, and identify a region of finite d-wave superconducting long-range order. With a lattice size of 50 sites we can reliably examine hole densities down to 0.16.