Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model

The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with M legs (with M ranging from 2 to 10) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity λ=8 in the charge and 2 λ=16 in the spin can be stabilized at doping δ=1/8. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with λ=6, appears at δ=1/6. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at δ=1/12and metallic with strong superconducting correlations at δ=1/10, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.