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

The authors employ the density-matrix renormalization group to investigate the doped Hubbard model on six-leg square cylinders. It uncovers a rich quantum phase diagram, intricately sensitive to next-nearest-neighbor electron hopping (t'). The positive-t' region shows a robust d-wave superconducting phase with intertwined superconducting and charge-density-wave orders. In contrast, the negative-t' side remains insulating, where doped holes form either long-range charge stripe order at small t' or a holon Wigner crystal with one doped hole per emergent unit cell and short-range spin correlations at larger t'.