  We study the ground state properties of the Hubbard model on a 4-leg cylinder
with doped hole concentration per site $\delta\leq 12.5\%$ using density-matrix
renormalization group. By keeping a large number of states for long system
sizes, we find that the nature of the ground state is remarkably sensitive to
the presence of next-nearest-neighbor hopping $t'$. Without $t'$ the ground
state of the system corresponds with the insulating filled stripe phase with
long-range charge-density-wave (CDW) order and short-range incommensurate spin
correlations appears. However, for a small negative $t'$ a phase characterized
by coexisting algebraic d-wave superconducting (SC)- and algebraic CDW
correlations. In addition, it shows short range spin- and fermion correlations
consistent with a canonical Luther-Emery (LE) liquid, except that the charge-
and spin periodicities are consistent with half-filled stripes instead of the
$4 k_F$ and $2 k_F$ wavevectors generic for one dimensional chains. For a small
positive $t'$ yet another phase takes over showing similar SC and CDW
correlations. However, the fermions are now characterized by a (near) infinite
correlation length while the gapped spin system is characterized by simple
staggered antiferromagnetic correlations. We will show that this is consistent
with a LE formed from a weakly coupled (BCS like) d-wave superconductor on the
ladder where the interactions have only the effect to stabilize a cuprate style
magnetic resonance.
