Ground-state phase diagram and superconductivity of the doped Hubbard model on six-leg square cylinders

We have studied the ground state properties of Hubbard model on long six-leg square cylinders with doped hole concentration 5.55% 8 12.5% using density-matrix renormalization group. Our state-of-the-art DMRG study with a large number of states convincingly shows that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor electron hopping t'. In the positive t' side, we find a robust d-wave superconducting (SC) phase characterized by coexisting quasi-long-range SC and charge density wave (CDW) correlations. Without t' the ground state forms an insulating stripe phase with long-range CDW order. In stark contrast to four-leg cylinders, our results show that the lightly doped Hubbard model on six-leg cylinders remains insulating in the negative t' side where the SC correlations decay exponentially with short correlation lengths. In the larger negative t' side, the doped holes form a holon Wigner crystal with one doped hole per emergent unit cell and short-range spin-spin correlations.