Ground state phase diagram of the doped Hubbard model on the four-leg cylinder

Abstract

We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site δ≤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 to 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 4k_{F} and 2k_{F} wave vectors that are 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 (nearly) 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 liquid formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect of stabilizing a cuprate style magnetic resonance.