Superconductivity in the t-J model on the square lattice

We report a density-matrix renormalization group study of lightly hole-doped t-J model on the square lattice. We observe an interesting interplay between d-wave superconductivity and spin and charge density wave (CDW) order. Despite the tendency of CDW order is strong, our results on finite-width cylinders strongly suggest that the ground state of the system is a Luther-Emery liquid with gapped spin excitation. There is no long-range CDW order no matter its pattern is commensurate or incommensurate. Moreover, we find that the superconducting pair-pair correlation decays power-law with an exponent close to one. The connection of our results to two dimensions is also discussed.