Ground state phase diagram of the doped Hubbard model on a two-leg ladder*

We have revisited the problem of the two-leg Hubbard ladder using DMRG methods but keeping larger number of states than in previous studies so as to obtain definitive results on the long-distance behavior of relevant ground-state correlation functions. In light of recent evidence that relatively small changes in the ratio of next nearest height for nearest neighbor hopping matrix, t'/t, can cause transitions between distinct ground-state phases, we have studied the model for a range of t'/t, electron density per site, n, and for several "intermediate" values of U/t. We find for a broad range of t'/t the ground-state exhibits quasi-long-range singlet superconducting order. For t'/t negative and large enough, two additional phases are found: One is characterized by commensurate charge-density-wave long-range order and a single gapless spin mode. Unexpectedly, for a relatively narrow range of negative t'/t, there exists an exotic intermediate phase with gapless charge and spin excitations, but one less gapless mode than for the non-interacting system.