Ground state phase diagram of doped Hubbard model on 4-leg cylinders*

We report a large-scale density-matrix renormalization group study of the lightly doped Hubbard model on 4-leg cylinders in the presence of next-nearest hopping t'. By keeping a large number of states for long system sizes, we are able to reveal a rich phase diagram consisting of a variety of distinct phases, including (1) The Luther-Emery (LE) liquid with quasi-long-range superconductivity (SC) and charge-density-wave (CDW) order, but with a gap in the spin sector; (2) Insulating phase with "filled" charge stripe and long-range CDW order but no long-range SC, and (3) Luttinger liquid phase with dominant single-particle correlation and subdominant SC and CDW correlations. In particular, at δ=12.5% doping concentration, we found that a tiny t'∼-0.01t is enough to drive the system out of the insulating state at t'=0 to the LE phase. Aside from t', the effect of Coulomb repulsion and doping concentration has also been explored. Our results indicate that a route to robust long-range superconductivity involves destabilizing insulating charge stripes in the doped Hubbard model.