Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t ′

The Hubbard model is widely believed to contain the essential ingredients of high-temperature superconductivity. Yet, proving definitively that the model supports superconductivity is challenging. Here, we report a large-scale density matrix renormalization group study of the lightly doped Hubbard model on four-leg cylinders at hole doping concentration δ = 12.5%. We reveal a delicate interplay between superconductivity and charge density wave and spin density wave orders tunable via next-nearest neighbor hopping t^$\prime$. For finite t^$\prime$, the ground state is consistent with a Luther-Emery liquid with power-law superconducting and charge density wave correlations associated with half-filled charge stripes. In contrast, for t^$\prime$ = 0, superconducting correlations fall off exponentially, whereas charge density and spin density modulations are dominant. Our findings suggest that a route to robust long-range superconductivity involves destabilizing insulating charge stripes in the doped Hubbard model.